Question

Substituting Values for Variables
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

Start with (4 m^(−3) n^2)^2 = 4^2 m^(−6) n^4.

Substitute m = 2, n = −3:
4^2 · 2^(−6) · (−3)^4 = 16 · (1/64) · 81 = (16·81)/64 = 81/4.

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