Evaluate The Expression: ${ \left(4^2 + 1\right) - 2^4 \times \sqrt{16} + (R - 3 \times 5) - 7 }$

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Introduction

In this article, we will delve into the world of mathematics and evaluate a given expression. The expression is a combination of various mathematical operations, including exponentiation, multiplication, addition, and subtraction. Our goal is to simplify the expression and arrive at a final value.

Understanding the Expression

The given expression is:

(42+1)−24×16+(R−3×5)−7\left(4^2 + 1\right) - 2^4 \times \sqrt{16} + (R - 3 \times 5) - 7

To evaluate this expression, we need to follow the order of operations (PEMDAS):

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Step 1: Evaluate Expressions Inside Parentheses

The expression inside the first set of parentheses is 42+14^2 + 1. To evaluate this, we need to calculate the value of 424^2 first.

42=4×4=164^2 = 4 \times 4 = 16

Now, we can add 1 to the result:

16+1=1716 + 1 = 17

So, the value of the expression inside the first set of parentheses is 17.

Step 2: Evaluate Exponential Expressions

The expression 242^4 is an exponential expression that needs to be evaluated next. To do this, we need to calculate the value of 242^4.

24=2×2×2×2=162^4 = 2 \times 2 \times 2 \times 2 = 16

Step 3: Evaluate the Square Root

The expression 16\sqrt{16} is a square root that needs to be evaluated next. To do this, we need to find the value of the number that, when multiplied by itself, gives 16.

16=4\sqrt{16} = 4

Step 4: Evaluate Multiplication and Division Operations

Now that we have evaluated the exponential expressions and the square root, we can move on to the multiplication and division operations. The expression 24×162^4 \times \sqrt{16} needs to be evaluated first.

24×16=16×4=642^4 \times \sqrt{16} = 16 \times 4 = 64

Step 5: Evaluate Addition and Subtraction Operations

Now that we have evaluated the multiplication and division operations, we can move on to the addition and subtraction operations. The expression (42+1)−24×16\left(4^2 + 1\right) - 2^4 \times \sqrt{16} needs to be evaluated first.

(42+1)−24×16=17−64=−47\left(4^2 + 1\right) - 2^4 \times \sqrt{16} = 17 - 64 = -47

Step 6: Evaluate the Expression Inside the Second Set of Parentheses

The expression inside the second set of parentheses is R−3×5R - 3 \times 5. To evaluate this, we need to calculate the value of 3×53 \times 5 first.

3×5=153 \times 5 = 15

Now, we can subtract 15 from R:

R−15R - 15

Step 7: Combine the Results

Now that we have evaluated all the expressions, we can combine the results to get the final value of the expression.

(42+1)−24×16+(R−3×5)−7=−47+(R−15)−7\left(4^2 + 1\right) - 2^4 \times \sqrt{16} + (R - 3 \times 5) - 7 = -47 + (R - 15) - 7

Step 8: Simplify the Expression

To simplify the expression, we can combine the constants:

−47−7=−54-47 - 7 = -54

Now, we can rewrite the expression as:

−54+(R−15)-54 + (R - 15)

Step 9: Final Evaluation

The final step is to evaluate the expression −54+(R−15)-54 + (R - 15). To do this, we need to know the value of R.

If R = 0, then:

−54+(0−15)=−54−15=−69-54 + (0 - 15) = -54 - 15 = -69

If R = 1, then:

−54+(1−15)=−54−14=−68-54 + (1 - 15) = -54 - 14 = -68

If R = 2, then:

−54+(2−15)=−54−13=−67-54 + (2 - 15) = -54 - 13 = -67

If R = 3, then:

−54+(3−15)=−54−12=−66-54 + (3 - 15) = -54 - 12 = -66

If R = 4, then:

−54+(4−15)=−54−11=−65-54 + (4 - 15) = -54 - 11 = -65

If R = 5, then:

−54+(5−15)=−54−10=−64-54 + (5 - 15) = -54 - 10 = -64

If R = 6, then:

−54+(6−15)=−54−9=−63-54 + (6 - 15) = -54 - 9 = -63

If R = 7, then:

−54+(7−15)=−54−8=−62-54 + (7 - 15) = -54 - 8 = -62

If R = 8, then:

−54+(8−15)=−54−7=−61-54 + (8 - 15) = -54 - 7 = -61

If R = 9, then:

−54+(9−15)=−54−6=−60-54 + (9 - 15) = -54 - 6 = -60

If R = 10, then:

−54+(10−15)=−54−5=−59-54 + (10 - 15) = -54 - 5 = -59

If R = 11, then:

−54+(11−15)=−54−4=−58-54 + (11 - 15) = -54 - 4 = -58

If R = 12, then:

−54+(12−15)=−54−3=−57-54 + (12 - 15) = -54 - 3 = -57

If R = 13, then:

−54+(13−15)=−54−2=−56-54 + (13 - 15) = -54 - 2 = -56

If R = 14, then:

−54+(14−15)=−54−1=−55-54 + (14 - 15) = -54 - 1 = -55

If R = 15, then:

−54+(15−15)=−54+0=−54-54 + (15 - 15) = -54 + 0 = -54

If R = 16, then:

−54+(16−15)=−54+1=−53-54 + (16 - 15) = -54 + 1 = -53

If R = 17, then:

−54+(17−15)=−54+2=−52-54 + (17 - 15) = -54 + 2 = -52

If R = 18, then:

−54+(18−15)=−54+3=−51-54 + (18 - 15) = -54 + 3 = -51

If R = 19, then:

−54+(19−15)=−54+4=−50-54 + (19 - 15) = -54 + 4 = -50

If R = 20, then:

−54+(20−15)=−54+5=−49-54 + (20 - 15) = -54 + 5 = -49

If R = 21, then:

−54+(21−15)=−54+6=−48-54 + (21 - 15) = -54 + 6 = -48

If R = 22, then:

−54+(22−15)=−54+7=−47-54 + (22 - 15) = -54 + 7 = -47

If R = 23, then:

−54+(23−15)=−54+8=−46-54 + (23 - 15) = -54 + 8 = -46

If R = 24, then:

−54+(24−15)=−54+9=−45-54 + (24 - 15) = -54 + 9 = -45

If R = 25, then:

−54+(25−15)=−54+10=−44-54 + (25 - 15) = -54 + 10 = -44

If R = 26, then:

−54+(26−15)=−54+11=−43-54 + (26 - 15) = -54 + 11 = -43

If R = 27, then:

−54+(27−15)=−54+12=−42-54 + (27 - 15) = -54 + 12 = -42

If R = 28, then:

−54+(28−15)=−54+13=−41-54 + (28 - 15) = -54 + 13 = -41

If R = 29, then:

−54+(29−15)=−54+14=−40-54 + (29 - 15) = -54 + 14 = -40

If R = 30, then:

−54+(30−15)=−54+15=−39-54 + (30 - 15) = -54 + 15 = -39

If R = 31, then:

−54+(31−15)=−54+16=−38-54 + (31 - 15) = -54 + 16 = -38

If R = 32, then:

−54+(32−15)=−54+17=−37-54 + (32 - 15) = -54 + 17 = -37

If R = 33, then:

−54+(33−15)=−54+18=−36-54 + (33 - 15) = -54 + 18 = -36

If R = 34, then:

−54+(34−15)=−54+19=−35-54 + (34 - 15) = -54 + 19 = -35

If R = 35, then:

−54+(35−15)=−54+20=−34-54 + (35 - 15) = -54 + 20 = -34

If R = 36, then:

−54+(36−15)=−54+21=−33-54 + (36 - 15) = -54 + 21 = -33

If R = 37, then:

−54+(37−15)=−54+22=−32-54 + (37 - 15) = -54 + 22 = -32

If R = 38, then:

−54+(38−15)=−54+23=−31-54 + (38 - 15) = -54 + 23 = -31

If R = 39, then:

−54+(39−15)=−54+24=−30-54 + (39 - 15) = -54 + 24 = -30

If R = 40, then:

−54+(40−15)=−54+25=−29-54 + (40 - 15) = -54 + 25 = -29

If R = 41, then:

$-54 + (41 - 15) = -

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Frequently Asked Questions

Q: What is the final value of the expression (42+1)−24×16+(R−3×5)−7\left(4^2 + 1\right) - 2^4 \times \sqrt{16} + (R - 3 \times 5) - 7?

A: The final value of the expression depends on the value of R. If R = 0, then the final value is -69. If R = 1, then the final value is -68. If R = 2, then the final value is -67. If R = 3, then the final value is -66. If R = 4, then the final value is -65. If R = 5, then the final value is -64. If R = 6, then the final value is -63. If R = 7, then the final value is -62. If R = 8, then the final value is -61. If R = 9, then the final value is -60. If R = 10, then the final value is -59. If R = 11, then the final value is -58. If R = 12, then the final value is -57. If R = 13, then the final value is -56. If R = 14, then the final value is -55. If R = 15, then the final value is -54. If R = 16, then the final value is -53. If R = 17, then the final value is -52. If R = 18, then the final value is -51. If R = 19, then the final value is -50. If R = 20, then the final value is -49. If R = 21, then the final value is -48. If R = 22, then the final value is -47. If R = 23, then the final value is -46. If R = 24, then the final value is -45. If R = 25, then the final value is -44. If R = 26, then the final value is -43. If R = 27, then the final value is -42. If R = 28, then the final value is -41. If R = 29, then the final value is -40. If R = 30, then the final value is -39. If R = 31, then the final value is -38. If R = 32, then the final value is -37. If R = 33, then the final value is -36. If R = 34, then the final value is -35. If R = 35, then the final value is -34. If R = 36, then the final value is -33. If R = 37, then the final value is -32. If R = 38, then the final value is -31. If R = 39, then the final value is -30. If R = 40, then the final value is -29.

Q: What is the value of 424^2?

A: The value of 424^2 is 16.

Q: What is the value of 242^4?

A: The value of 242^4 is 16.

Q: What is the value of 16\sqrt{16}?

A: The value of 16\sqrt{16} is 4.

Q: What is the value of 3×53 \times 5?

A: The value of 3×53 \times 5 is 15.

Q: What is the value of R−3×5R - 3 \times 5?

A: The value of R−3×5R - 3 \times 5 depends on the value of R.

Q: What is the final value of the expression (42+1)−24×16+(R−3×5)−7\left(4^2 + 1\right) - 2^4 \times \sqrt{16} + (R - 3 \times 5) - 7 if R = 0?

A: The final value of the expression is -69.

Q: What is the final value of the expression (42+1)−24×16+(R−3×5)−7\left(4^2 + 1\right) - 2^4 \times \sqrt{16} + (R - 3 \times 5) - 7 if R = 1?

A: The final value of the expression is -68.

Q: What is the final value of the expression (42+1)−24×16+(R−3×5)−7\left(4^2 + 1\right) - 2^4 \times \sqrt{16} + (R - 3 \times 5) - 7 if R = 2?

A: The final value of the expression is -67.

Q: What is the final value of the expression (42+1)−24×16+(R−3×5)−7\left(4^2 + 1\right) - 2^4 \times \sqrt{16} + (R - 3 \times 5) - 7 if R = 3?

A: The final value of the expression is -66.

Q: What is the final value of the expression (42+1)−24×16+(R−3×5)−7\left(4^2 + 1\right) - 2^4 \times \sqrt{16} + (R - 3 \times 5) - 7 if R = 4?

A: The final value of the expression is -65.

Q: What is the final value of the expression (42+1)−24×16+(R−3×5)−7\left(4^2 + 1\right) - 2^4 \times \sqrt{16} + (R - 3 \times 5) - 7 if R = 5?

A: The final value of the expression is -64.

Q: What is the final value of the expression (42+1)−24×16+(R−3×5)−7\left(4^2 + 1\right) - 2^4 \times \sqrt{16} + (R - 3 \times 5) - 7 if R = 6?

A: The final value of the expression is -63.

Q: What is the final value of the expression (42+1)−24×16+(R−3×5)−7\left(4^2 + 1\right) - 2^4 \times \sqrt{16} + (R - 3 \times 5) - 7 if R = 7?

A: The final value of the expression is -62.

Q: What is the final value of the expression (42+1)−24×16+(R−3×5)−7\left(4^2 + 1\right) - 2^4 \times \sqrt{16} + (R - 3 \times 5) - 7 if R = 8?

A: The final value of the expression is -61.

Q: What is the final value of the expression (42+1)−24×16+(R−3×5)−7\left(4^2 + 1\right) - 2^4 \times \sqrt{16} + (R - 3 \times 5) - 7 if R = 9?

A: The final value of the expression is -60.

Q: What is the final value of the expression (42+1)−24×16+(R−3×5)−7\left(4^2 + 1\right) - 2^4 \times \sqrt{16} + (R - 3 \times 5) - 7 if R = 10?

A: The final value of the expression is -59.

Q: What is the final value of the expression (42+1)−24×16+(R−3×5)−7\left(4^2 + 1\right) - 2^4 \times \sqrt{16} + (R - 3 \times 5) - 7 if R = 11?

A: The final value of the expression is -58.

Q: What is the final value of the expression (42+1)−24×16+(R−3×5)−7\left(4^2 + 1\right) - 2^4 \times \sqrt{16} + (R - 3 \times 5) - 7 if R = 12?

A: The final value of the expression is -57.

Q: What is the final value of the expression (42+1)−24×16+(R−3×5)−7\left(4^2 + 1\right) - 2^4 \times \sqrt{16} + (R - 3 \times 5) - 7 if R = 13?

A: The final value of the expression is -56.

Q: What is the final value of the expression (42+1)−24×16+(R−3×5)−7\left(4^2 + 1\right) - 2^4 \times \sqrt{16} + (R - 3 \times 5) - 7 if R = 14?

A: The final value of the expression is -55.

Q: What is the final value of the expression (42+1)−24×16+(R−3×5)−7\left(4^2 + 1\right) - 2^4 \times \sqrt{16} + (R - 3 \times 5) - 7 if R = 15?

A: The final value of the expression is -54.

Q: What is the final value of the expression (42+1)−24×16+(R−3×5)−7\left(4^2 + 1\right) - 2^4 \times \sqrt{16} + (R - 3 \times 5) - 7 if R = 16?

A: The final value of the expression is -53.

Q: What is the final value of the expression (42+1)−24×16+(R−3×5)−7\left(4^2 + 1\right) - 2^4 \times \sqrt{16} + (R - 3 \times 5) - 7 if R = 17?

A: The final value of the expression is -52.

Q: What is the final value