QuestionSimplify $\left(m^{-9} p^{5}\right)^{-4}$ with positive exponents. What is the result?

Studdy Solution
Assumptions. All variables represent positive real numbers.
2. We are required to write the answer with only positive exponents.
2We start by applying the power of a power rule, which states that when raising a power to a power, we multiply the exponents.$$\left(m^{-9} p^{5}\right)^{-4} = m^{-9 \times -4} p^{5 \times -4}$$3Now we can calculate the new exponents.
$$m^{-9 \times -4} p^{5 \times -4} = m^{36} p^{-20}$$4The problem requires us to write the answer with only positive exponents. Therefore, we need to convert $p^{-20}$ to a positive exponent. We can do this by moving it to the denominator.$$m^{36} p^{-20} = \frac{m^{36}}{p^{20}}$$This is the simplified form of the expression with positive exponents.