Question

Study the expression. What is the value of the expression when m=2 and n= –3?

(4m–3n2)2

1. Apply the power of a power:      42 m–6n4

2. Substitute values for variables:     (4)2(2)–6(–3)4

3. Apply the negative exponent:      
(4)2(−3)4
26

Complete the steps to evaluate the expression.
Written as an improper fraction, the expression has a value of
.

Answer 1

Interpret the expression as (4m^(-3) n^2)^2.

1. Apply the power: (4m^(-3)n^2)^2 = 4^2 m^(-6) n^4.
2. Substitute m = 2, n = −3: 4^2·2^(−6)·(−3)^4 = (4^2·(−3)^4) / 2^6.
3. Evaluate: 4^2 = 16, (−3)^4 = 81, 2^6 = 64, so the value is 16·81/64 = 1296/64 = 81/4.

Written as an improper fraction the value is 81/4.