Using the Power Rule of Exponents, what is the exponent of \( \left(7^{2}\right)^{2} \) in exponential simplest form if the base remains 7 ? (1 point)

To solve \( \left(7^{2}\right)^{2} \) using the Power Rule of Exponents, recall that the Power Rule states:

\[
\left(a^m\right)^n = a^{m \cdot n}
\]

In this case, the base \(a = 7\), and the exponents are \(m = 2\) and \(n = 2\). Applying the Power Rule:

\[
\left(7^2\right)^2 = 7^{2 \cdot 2} = 7^4
\]

Thus, the exponent of \( 7^4 \) in exponential simplest form is **4**.

Would you like a more detailed explanation?

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Here are 5 related questions to expand your understanding:

1. How would you simplify \( \left(3^5\right)^3 \) using the Power Rule?
2. What is the result of \( \left(2^4\right)^3 \)?
3. Can the Power Rule be applied to variables, such as \( \left(x^3\right)^4 \)?
4. How would you combine \( 7^3 \cdot 7^4 \) using exponent rules?
5. What happens if you raise a number with an exponent of 1, like \( \left(7^1\right)^3 \)?

**Tip:** The Power Rule can be extended to any situation where you are raising a power to another power, even when using variables or complex expressions!

Using the Power Rule of Exponents, what is the exponent of \( \left(7^{2}\right)^{2} \) in exponential simplest form if the base remains 7?

Understand how to simplify the expression \( (7^2)^2 \) using the Power Rule of Exponents. This step-by-step guide helps students in Grades 6-8 apply exponent rules to solve similar problems.

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