Simplify. Express your answer using exponents. (t^(-6)u^(2)v^(8))^(-6)

Identify Operation: Identify the operation to be performed on the exponents. When raising a power to a power, we multiply the exponents.Apply Power: Apply the power to each exponent inside the parentheses. (t^(-6)u^(2)v^(8))^(-6) becomes t^(-6 * -6) * u^(2 * -6) * v^(8 * -6).Perform Multiplication: Perform the multiplication of the exponents. t^(-6 * -6) becomes t^(36). u^(2 * -6) becomes u^(-12). v^(8 * -6) becomes v^(-48).Express Exponents: Express the negative exponents as positive exponents. Since u^(-12) and v^(-48) have negative exponents, we can write them as 1/u^(12) and 1/v^(48) respectively.Combine Results: Combine the results to express the final answer. The simplified expression is t^(36) * 1/u^(12) * 1/v^(48), or t^(36) / (u^(12)v^(48)).

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Math Problems

Algebra 1

Simplify exponential expressions using exponent rules

Full solution

Q. Simplify. Express your answer using exponents.

\newline

\left(t^{-6} u^{2} v^{8}\right)^{-6}

Identify Operation: Identify the operation to be performed on the exponents. $\newline$ When raising a power to a power, we multiply the exponents.
Apply Power: Apply the power to each exponent inside the parentheses. $\newline$ $(t^{-6}u^{2}v^{8})^{-6}$ becomes $t^{(-6 \times -6)} \times u^{(2 \times -6)} \times v^{(8 \times -6)}.$
Perform Multiplication: Perform the multiplication of the exponents. $\newline$ $t^{(-6 \times -6)}$ becomes $t^{36}$ . $\newline$ $u^{(2 \times -6)}$ becomes $u^{-12}$ . $\newline$ $v^{(8 \times -6)}$ becomes $v^{-48}$ .
Express Exponents: Express the negative exponents as positive exponents. $\newline$ Since $u^{-12}$ and $v^{-48}$ have negative exponents, we can write them as $\frac{1}{u^{12}}$ and $\frac{1}{v^{48}}$ respectively.
Combine Results: Combine the results to express the final answer. $\newline$ The simplified expression is $t^{36} \times \frac{1}{u^{12}} \times \frac{1}{v^{48}}$ , or $\frac{t^{36}}{u^{12}v^{48}}$ .