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

(81x^(-6)y^(2))^((1)/(2))
Answer:

Simplify the following expression to simplest form using only positive exponents. $\newline$ $\left(81 x^{-6} y^{2}\right)^{\frac{1}{2}}$ $\newline$ Answer:

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Multiplication with rational exponents

Full solution

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

\newline

\left(81 x^{-6} y^{2}\right)^{\frac{1}{2}}

\newline

Answer:

Apply Exponent Rule: Apply the exponent rule $(a^m)^n = a^{m*n}$ to the given expression. $\newline$ $(81x^{-6}y^{2})^{\frac{1}{2}} = 81^{\frac{1}{2}} * x^{-6*\frac{1}{2}} * y^{2*\frac{1}{2}}$
Simplify Parts: Simplify each part of the expression separately. $\newline$ $81^{\frac{1}{2}} = 9$ because $9^2 = 81$ $\newline$ $x^{-6\left(\frac{1}{2}\right)} = x^{-3}$ because $-6\left(\frac{1}{2}\right) = -3$ $\newline$ $y^{2\left(\frac{1}{2}\right)} = y^1 = y$ because $2\left(\frac{1}{2}\right) = 1$
Rewrite with Positive Exponents: Rewrite the expression with positive exponents by moving the term with a negative exponent to the denominator. $\newline$ $9 \times x^{-3} \times y = \frac{9y}{x^3}$ because $x^{-3} = \frac{1}{x^3}$
Combine Simplified Parts: Combine the simplified parts to write the final answer. $\newline$ The expression $(81x^{-6}y^{2})^{\frac{1}{2}}$ simplifies to $\frac{9y}{x^3}$ .

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