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Simplify. Assume all variables are positive. $\newline$ $(27x)^{\frac{2}{3}}$ $\newline$ $\newline$ Write your answer in the form $A$ or $\frac{A}{B}$ , where $A$ and $B$ are constants or variable expressions that have no variables in common. All exponents in your answer should be positive. $\newline$ ______

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Q. Simplify. Assume all variables are positive.

\newline

(27x)^{\frac{2}{3}}

\newline

\newline

Write your answer in the form

A

or

\frac{A}{B}

, where

A

and

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

______

Identify Expression: Identify the expression to simplify. $\newline$ We have the expression $(27x)^{\frac{2}{3}}$ which we need to simplify.
Break Down Components: Break down the expression into its components. $\newline$ The expression $(27x)^{\frac{2}{3}}$ can be rewritten as $27^{\frac{2}{3}} \times x^{\frac{2}{3}}$ because when you have a power of a product, you can apply the exponent to each factor separately.
Simplify $27^{\frac{2}{3}}$ : Simplify $27^{\frac{2}{3}}$ . We know that $27$ is $3^3$ , so we can rewrite $27^{\frac{2}{3}}$ as $(3^3)^{\frac{2}{3}}$ . When raising a power to another power, we multiply the exponents, so $(3^3)^{\frac{2}{3}}$ becomes $3^{3*\frac{2}{3}}$ which simplifies to $3^2$ .
Calculate $3^2$ : Calculate $3^2$ . $3^2$ is $3$ multiplied by itself, which equals $9$ .
Combine Simplified Components: Combine the simplified components. $\newline$ Now we have $9 \times x^{\frac{2}{3}}$ . Since there are no further simplifications possible, this is the final simplified form of the expression.

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