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

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 2

without ()[]{}

Answer 3

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 4

try again

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).