What is the exponent in an equivalent form of the expression (8^3)^3
?(1 point)

To solve the expression \((8^3)^3\), we apply the **power of a power rule**, which states:

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

Here, \(a = 8\), \(m = 3\), and \(n = 3\). So we multiply the exponents:

\[
(8^3)^3 = 8^{3 \cdot 3} = 8^9
\]

Thus, the exponent in the equivalent form of the expression is **9**.

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Would you like more details or have any questions?

Here are some related questions:
1. What is the value of \(8^9\)?
2. How would you simplify \((2^4)^5\) using the power of a power rule?
3. Can you apply the power of a power rule to variables like \((x^5)^3\)?
4. What happens if the base is negative in an expression like \((-2^2)^3\)?
5. How does the power of a product rule differ from the power of a power rule?

**Tip:** Remember that when raising a power to another power, you always **multiply** the exponents!

What is the exponent in an equivalent form of the expression (8^3)^3?

Discover how to solve (8^3)^3 using the power of a power rule. This problem illustrates the key exponent rules, where multiplying exponents is crucial. The solution is appropriate for students in Grades 8-10 and involves basic exponent laws.

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