Question

(2b^-5)^3
Which of the following is equivalent to the given expression for all b ≠ 0

Answer 1

To simplify the expression \((2b^{-5})^3\), we can apply the power of a product rule and the power of a power rule in exponents:

1. Apply the power of a product:
\[
(2b^{-5})^3 = 2^3 \cdot (b^{-5})^3
\]

2. Calculate \(2^3\) and simplify \((b^{-5})^3\):
\[
2^3 = 8
\]
\[
(b^{-5})^3 = b^{-15}
\]

3. Combine the two results:
\[
8b^{-15}
\]

4. Since \(b^{-15}\) can also be expressed as \(\frac{1}{b^{15}}\), we can write the final expression as:
\[
8b^{-15} = \frac{8}{b^{15}}
\]

Hence, the expression \((2b^{-5})^3\) simplifies to:

\[
8b^{-15} \quad \text{or} \quad \frac{8}{b^{15}}
\]

This is equivalent for all \(b \neq 0\).