Question

simplify. express your answer using exponents.
$(a^{10}b^{-5})^{3}$

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((xy)^n = x^n y^n\). So, for \((a^{10}b^{-5})^3\), we can apply this rule to get \( (a^{10})^3 \cdot (b^{-5})^3 \).

Step2: Apply power of a power rule

The power of a power rule is \((x^m)^n = x^{m \cdot n}\). Applying this to each term:

• For \((a^{10})^3\), we have \(a^{10 \cdot 3} = a^{30}\).
• For \((b^{-5})^3\), we have \(b^{-5 \cdot 3} = b^{-15}\).

Step3: Combine the terms

Putting the two results together, we get \(a^{30}b^{-15}\).

Answer:

\(a^{30}b^{-15}\)