Question

simplify. express your answer using exponents.
$(m^{-8}n^{9}p^{12})^{2}$

Explanation:

Step1: Apply power of a product rule

To simplify \((m^{-8}n^{9}p^{12})^{2}\), we use the power of a product rule \((ab)^n = a^n b^n\). So we apply the exponent 2 to each factor inside the parentheses:
\(m^{-8\times2}n^{9\times2}p^{12\times2}\)

Step2: Multiply the exponents

Calculate the exponents for each variable:

• For \(m\): \(-8\times2 = -16\), so we have \(m^{-16}\)
• For \(n\): \(9\times2 = 18\), so we have \(n^{18}\)
• For \(p\): \(12\times2 = 24\), so we have \(p^{24}\)

Combining these, the simplified form is \(m^{-16}n^{18}p^{24}\) (if we want to keep negative exponents) or we could write it with positive exponents as \(\frac{n^{18}p^{24}}{m^{16}}\), but since the problem just says to express using exponents (and negative exponents are allowed in exponent form), the simplified form with exponents is \(m^{-16}n^{18}p^{24}\)

Answer:

\(m^{-16}n^{18}p^{24}\)