Question

simplify. express your answer using exponents.
$(d^{11}g^{-10}h^{-8})^{7}$

Explanation:

Step1: Apply Power of a Product Rule

The power of a product rule states that \((ab)^n = a^n b^n\). So, for \((d^{11}g^{-10}h^{-8})^{7}\), we apply this rule to each factor:
\(d^{11\times7}g^{-10\times7}h^{-8\times7}\)

Step2: Calculate Each Exponent

• For the \(d\) term: \(11\times7 = 77\), so we have \(d^{77}\).
• For the \(g\) term: \(- 10\times7=-70\), so we have \(g^{-70}\).
• For the \(h\) term: \(-8\times7 = - 56\), so we have \(h^{-56}\).

Answer:

\(d^{77}g^{-70}h^{-56}\)