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Simplify the following expression to simplest form using only positive exponents.

(32x^(10)y^(5))^(-(1)/(5))
Answer:

Simplify the following expression to simplest form using only positive exponents. $\newline$ $\left(32 x^{10} y^{5}\right)^{-\frac{1}{5}}$ $\newline$ Answer:

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Evaluate integers raised to rational exponents

Full solution

Q. Simplify the following expression to simplest form using only positive exponents.

\newline

\left(32 x^{10} y^{5}\right)^{-\frac{1}{5}}

\newline

Answer:

Understand Problem: Understand the problem and apply the negative exponent rule. $\newline$ The negative exponent rule states that $a^{-n} = \frac{1}{a^n}$ . We will apply this rule to the entire expression.
Apply Negative Exponent Rule: Apply the negative exponent rule to the expression. $\newline$ $(32x^{10}y^{5})^{-(1)/(5)} = \frac{1}{(32x^{10}y^{5})^{1/5}}$
Simplify Expression Inside Parentheses: Simplify the expression inside the parentheses by taking the fifth root. $\newline$ The fifth root of $32$ is $2$ , because $2^5 = 32$ . $\newline$ The fifth root of $x^{10}$ is $x^{10/5} = x^2$ , because $(x^2)^5 = x^{2\cdot5} = x^{10}$ . $\newline$ The fifth root of $y^{5}$ is $y^{5/5} = y^1 = y$ , because $y^1 = y$ . $\newline$ $\frac{1}{(32x^{10}y^{5})^{1/5}} = \frac{1}{2x^2y}$
Write Final Simplified Expression: Write the final simplified expression with only positive exponents. $\newline$ The final expression is $\frac{1}{2x^2y}$ .

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