Question

simplify. express your answer using exponents.
$(t^{10}u^{8}v^{-12})^{2}$

Explanation:

Step1: Apply power of a product rule

To simplify \((t^{10}u^{8}v^{-12})^{2}\), we use the power of a product rule \((ab)^n = a^n b^n\) and the power of a power rule \((a^m)^n=a^{m\times n}\). So we raise each factor to the power of 2:
\(t^{10\times2}u^{8\times2}v^{- 12\times2}\)

Step2: Calculate the exponents

Calculate each exponent:
For \(t\): \(10\times2 = 20\), so we have \(t^{20}\)
For \(u\): \(8\times2=16\), so we have \(u^{16}\)
For \(v\): \(- 12\times2=-24\), so we have \(v^{-24}\)

Combining these, the simplified form is \(t^{20}u^{16}v^{-24}\)

Answer:

\(t^{20}u^{16}v^{-24}\)