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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

1 answer

Let's break down the expression step by step with \( m = 2 \) and \( n = -3 \).

Starting with the expression:

\[ (4m - 3n^2)^2 \]

  1. First, substitute values for \( m \) and \( n \): \[ m = 2 \quad \text{and} \quad n = -3 \] This gives us: \[ (4(2) - 3(-3)^2)^2 \]

  2. Calculate \( -3^2 \): \[ (-3)^2 = 9 \] Now the expression becomes: \[ (4(2) - 3(9))^2 \]

  3. Calculate \( 4(2) \): \[ 4(2) = 8 \] Now the expression is: \[ (8 - 3(9))^2 \]

  4. Calculate \( 3(9) \): \[ 3 \times 9 = 27 \] Thus, we have: \[ (8 - 27)^2 \]

  5. Calculate \( 8 - 27 \): \[ 8 - 27 = -19 \] Therefore, the expression now is: \[ (-19)^2 \]

  6. Finally, calculate \( (-19)^2 \): \[ (-19)^2 = 361 \]

So, the value of the expression when \( m = 2 \) and \( n = -3 \) is:

\[ \boxed{361} \]