Question

($\frac{2p^{2}}{3p^{7}}$)^{-2}
write your answer using only positive exponents.

Explanation:

Step1: Simplify the fraction inside the parentheses

Use the quotient - rule of exponents $\frac{a^m}{a^n}=a^{m - n}$. So, $\frac{2p^{2}}{3p^{7}}=\frac{2}{3}p^{2-7}=\frac{2}{3}p^{- 5}$.

Step2: Apply the power - of - a - product rule

$(ab)^n=a^n b^n$. So, $(\frac{2}{3}p^{-5})^{-2}=(\frac{2}{3})^{-2}(p^{-5})^{-2}$.

Step3: Calculate $(\frac{2}{3})^{-2}$

Use the negative - exponent rule $a^{-n}=\frac{1}{a^{n}}$. Then $(\frac{2}{3})^{-2}=\frac{3^{2}}{2^{2}}=\frac{9}{4}$.

Step4: Calculate $(p^{-5})^{-2}$

Use the power - of - a - power rule $(a^m)^n=a^{mn}$. So, $(p^{-5})^{-2}=p^{(-5)\times(-2)} = p^{10}$.

Step5: Combine the results

$(\frac{2}{3})^{-2}(p^{-5})^{-2}=\frac{9}{4}p^{10}$.

Answer:

$\frac{9p^{10}}{4}$