Evaluate the expression. [(3–5)(34)]3

Question

1 Innermost group, apply the product of powers: [3–1]3

2 Apply the power of a power:         3–3

3 Apply the negative exponent:         
1
33

4 Simplify:                  
1
x

What is the value of x in the simplified expression?
x=

Answer 1

Let's evaluate the expression step-by-step.

Original expression: \[ [(3-5)(34)]^3 \]

1. First, evaluate the innermost expression \(3 - 5\): \[ 3 - 5 = -2 \] Now the expression becomes: \[ [-2(34)]^3 \]

2. Next, evaluate \( -2 \times 34 \): \[ -2 \times 34 = -68 \] Now the expression is: \[ [-68]^3 \]

3. Calculate \((-68)^3\): \[ -68^3 = -68 \times -68 \times -68 \] We first calculate \(68^2\): \[ 68 \times 68 = 4624 \] Now, multiply that by \(-68\): \[ -68 \times 4624 = -314432 \]

So, the value of \([-68]^3\) is \(-314432\).

The final value of \(x\) in the expression is: \[ \boxed{-314432} \]