Question

Which expression is equivalent to 6, squared, times, left parenthesis, 6, to the power minus 6 , right parenthesis, squared, question mark6 2 ×(6 −6 ) 2 ?

Answer 1

without ()[]{}

Answer 2

try again

Answer 3

To simplify the expression \(6^2 \times (6^{-6})^2\), we can proceed as follows:

1. **Calculate \(6^2\)**:
\[
6^2 = 36
\]

2. **Simplify \((6^{-6})^2\)** using the property of exponents \((a^m)^n = a^{m \times n}\):
\[
(6^{-6})^2 = 6^{-12}
\]

3. **Combine the two parts**:
\[
6^2 \times (6^{-6})^2 = 6^2 \times 6^{-12}
\]

4. **Using the property of exponents \(a^m \times a^n = a^{m+n}\)**, we combine the exponents:
\[
6^{2 + (-12)} = 6^{-10}
\]

Thus, the expression \(6^2 \times (6^{-6})^2\) simplifies to:

\[
\boxed{6^{-10}}
\]

Answer 4

Sure! The expression can be simplified as follows:

1. Start with the expression: **6 squared times 6 to the power of -6 squared**.

2. This translates mathematically to: **6^2 × (6^-6)^2**.

3. Calculate each part:
- 6^2 = 36.
- (6^-6)^2 = 6^(-6 * 2) = 6^-12.

4. Now, combine these:
- 6^2 × 6^-12 = 6^(2 + (-12)) = 6^-10.

Thus, the simplified expression is:

**6^-10**.

Answer 5

Apologies for the misunderstanding. Let's go through it step by step again without using any parentheses.

The original expression is:

**6 squared times 6 to the power of -6 squared**

1. First, evaluate **6 squared**:
6 squared = 6^2

2. Next, evaluate **6 to the power of -6 squared**:
- Here, -6 squared means (6^-6) squared = (6^-6) * (6^-6) = 6^(-6 * 2) = 6^-12.

3. Now combine both parts:
- You now have **6^2 times 6^-12**.

4. Using the property of exponents where you add the exponents:
- 6^2 times 6^-12 = 6^(2 + (-12)) = 6^(-10).

Thus, the final equivalent expression is:

**6^(-10)**.