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

(49x^(2)y^(8))^(-(1)/(2))
Answer:

Simplify the following expression to simplest form using only positive exponents. $\newline$ $\left(49 x^{2} y^{8}\right)^{-\frac{1}{2}}$ $\newline$ 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(49 x^{2} y^{8}\right)^{-\frac{1}{2}}

\newline

Answer:

Apply negative exponent rule: 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. $\newline$ $(49x^{2}y^{8})^{-\frac{1}{2}} = \frac{1}{(49x^{2}y^{8})^{\frac{1}{2}}}$
Simplify inside parentheses: Simplify the expression inside the parentheses. $\newline$ We need to find the square root of each term inside the parentheses since the exponent is $\frac{1}{2}$ . $\newline$ The square root of $49$ is $7$ , the square root of $x^2$ is $x$ , and the square root of $y^8$ is $y^4$ . $\newline$ $\frac{1}{((49x^{2}y^{8})^{\frac{1}{2}})} = \frac{1}{(7x^{1}y^{4})}$
Write final expression: Write the final expression using only positive exponents. $\newline$ Since we have already applied the negative exponent as a reciprocal in step $1$ , the final expression is already with positive exponents. $\newline$ The final simplified expression is $\frac{1}{7x y^{4}}$ .

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