Question

practice using order of operations with expressions with exponents
study the example showing how to evaluate an expression with exponents and parentheses. then solve problems 1–6.
example
what is the value of the expression 4(5 - 2)² + 5³?
use the order of operations to evaluate the expression.
subtract inside the parentheses. 4(5 - 2)² + 5³ = 4(3)² + 5³
evaluate the powers. = 4(9) + 125
multiply. = 36 + 125
add = 161
1 what is the value of the expression 5(2³ - 3)? show your work.
solution
2 miguel writes the expression 2n⁴. he says that when you double the value of n, you double the value of the expression. do you agree or disagree? explain.
3 evaluate the expression 1⁴ + 3(10 - 2)². show your work.

Explanation:

Problem 1:

Step1: Evaluate exponent inside parentheses

First, calculate the exponent within the parentheses: \(2^3 = 8\). Then subtract 3 from that result: \(8 - 3 = 5\). So the expression becomes \(5\times5\) (wait, no, the original expression is \(5(2^3 - 3)\), so after evaluating inside the parentheses: \(2^3 - 3 = 8 - 3 = 5\).

Step2: Multiply

Now multiply 5 by the result from Step 1: \(5\times5 = 25\).

To determine if doubling \(n\) in \(2n^4\) doubles the expression, substitute \(2n\) for \(n\): \(2(2n)^4 = 2\times16n^4 = 32n^4\). The original expression is \(2n^4\). Doubling the original would be \(4n^4\), but \(32n^4\) is 16 times the original, not double. So disagree.

Step1: Evaluate exponents and parentheses

First, calculate the exponent \(1^4 = 1\). Then, inside the parentheses: \(10 - 2 = 8\), and its square: \(8^2 = 64\).

Step2: Multiply

Multiply 3 by 64: \(3\times64 = 192\).

Step3: Add

Add the result from Step 1 (1) to the result from Step 2 (192): \(1 + 192 = 193\).

Answer:

25

Problem 2: