Applying the Power Rule of Exponents, what is the exponent in an equivalent form of ((1/6)^3)^3

? Answer with a whole number for the exponent where the base is 16

1/6

.(1 point)

￼

To simplify \(\left( \left( \frac{1}{6} \right)^3 \right)^3\), we apply the **Power Rule of Exponents**, which states that \((a^m)^n = a^{m \cdot n}\).

Here, the base is \(\frac{1}{6}\), and we have:

\[
\left( \left( \frac{1}{6} \right)^3 \right)^3 = \left( \frac{1}{6} \right)^{3 \cdot 3} = \left( \frac{1}{6} \right)^9
\]

So, the exponent is **9**.

Would you like more details or have any questions?

Here are some related questions for further practice:

1. Simplify \(\left( \frac{2}{5} \right)^4\).
2. Apply the power rule to simplify \(\left( 3^2 \right)^4\).
3. What is the result of \(\left( 7^{-2} \right)^3\)?
4. If \(\left( x^4 \right)^5 = x^k\), what is \(k\)?
5. Simplify \(\left( \frac{3}{8} \right)^2\).

**Tip:** When using the power rule, always multiply the exponents if both are applied to the same base.

Applying the Power Rule of Exponents, what is the exponent in an equivalent form of ((1/6)^3)^3? Answer with a whole number for the exponent where the base is 1/6.

Understand how to apply the Power Rule of Exponents to simplify ((1/6)^3)^3. Learn the step-by-step process to find the final exponent using the formula (a^m)^n = a^{m * n}. This problem is ideal for students in Grades 6-8 and covers key concepts in algebra.

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