Question

simplify. express your answer using exponents.
$(u^{6}v^{9})^{-7}$

Explanation:

Step1: Apply power of a product rule

$(ab)^n = a^n b^n$
So, $(u^6 v^9)^{-7} = (u^6)^{-7} \cdot (v^9)^{-7}$

Step2: Apply power of a power rule

$(a^m)^n = a^{m \cdot n}$
For the $u$ term: $(u^6)^{-7} = u^{6 \times (-7)} = u^{-42}$
For the $v$ term: $(v^9)^{-7} = v^{9 \times (-7)} = v^{-63}$

Step3: Combine the terms

Multiply the simplified terms together.

Answer:

$u^{-42}v^{-63}$ (or equivalently $\frac{1}{u^{42}v^{63}}$)