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Write the following expression without negative exponents and without parentheses.

(-3x)^(-2)
Answer:

Write the following expression without negative exponents and without parentheses. $\newline$ $(-3 x)^{-2}$ $\newline$ Answer:

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Evaluate rational expressions

Full solution

Q. Write the following expression without negative exponents and without parentheses.

\newline

(-3 x)^{-2}

\newline

Answer:

Understand Negative Exponents: Understand the properties of negative exponents. The negative exponent rule states that $a^{-n} = \frac{1}{a^n}$ for any non-zero $a$ and positive integer $n$ . We will apply this rule to the expression $(-3x)^{-2}$ .
Apply Negative Exponent Rule: Apply the negative exponent rule to the expression. $\newline$ Using the rule from Step $1$ , we can rewrite $(-3x)^{-2}$ as $\frac{1}{((-3x)^2)}$ .
Simplify Expression Inside Parentheses: Simplify the expression inside the parentheses. $\newline$ When we square $(-3x)$ , we square both the coefficient and the variable. This gives us $(-3)^2 \times x^2$ .
Calculate Squares: Calculate the square of $-3$ and $x$ . $(-3)^2$ equals $9$ because the square of a negative number is positive. $x^2$ remains as it is. So, $(-3)^2 \times x^2$ becomes $9x^2$ .
Write Final Expression: Write the final expression without negative exponents and without parentheses. $\newline$ The final expression is $\frac{1}{9x^2}$ .

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