Question

Maggie tried to evaluate the expression (4^-3*4^6)^3
(4^-3*4^6)^3
=(4^3)^3 Step 1
=4^6 Step 2
=4,096 Step 3
Which statement is true?

Maggie made a mistake in step 1
Maggie made a mistake in step 2
Maggie made a mistake in step 3
Maggie did not make a mistake

Answer 1

Let's evaluate the expression step by step.

The original expression is \((4^{-3} \times 4^{6})^3\).

1. **Step 1:** Combine the exponents inside the parentheses.
\[
4^{-3} \times 4^{6} = 4^{(-3 + 6)} = 4^{3}
\]
So, we have \((4^3)^3\).

2. **Step 2:** Apply the power of a power property.
\[
(4^3)^3 = 4^{3 \times 3} = 4^9
\]

3. **Step 3:** Now calculate \(4^9\).
\[
4^9 = 262144
\]

Thus, the calculations show that Maggie made a mistake in step 1 by stating that \((4^{-3} \times 4^{6})^3 = (4^3)^3\). The correct result should be \(4^{9}\).

So, the true statement is:
**Maggie made a mistake in step 1.**