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Simplify.
(2)/((3x)^(-4))

Simplify. $\newline$ $\frac{2}{(3 x)^{-4}}$

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Evaluate rational exponents

Full solution

Q. Simplify.

\newline

\frac{2}{(3 x)^{-4}}

Identify base and exponent: Identify the base and the exponent in $(3x)^{-4}$ . $\newline$ In $(3x)^{-4}$ , the base is $3x$ and the exponent is $-4$ .
Apply negative exponent rule: Apply the negative exponent rule, which states that $a^{-n} = \frac{1}{a^n}$ . $\newline$ So, $(3x)^{-4}$ becomes $\frac{1}{(3x)^4}$ .
Multiply by reciprocal: Multiply the fraction $2$ by the reciprocal of $(3x)^{-4}$ . $\newline$ This gives us $2 \times \left(\frac{1}{(3x)^4}\right)$ .
Simplify expression by multiplication: Simplify the expression by multiplying the numerators and denominators. This results in $\frac{2}{(3x)^4}$ .
Expand denominator by raising powers: Expand the denominator $(3x)^4$ by raising both $3$ and $x$ to the power of $4$ . This gives us $\frac{2}{3^4 \times x^4}$ .
Calculate $3^4$ : Calculate $3^4$ to simplify the denominator further. $\newline$ $3^4$ equals $81$ .
Substitute $81$ in denominator: Substitute $81$ for $3^4$ in the denominator. $\newline$ This gives us $2/(81 \times x^4)$ .
Final simplified answer: The expression is now fully simplified, and there are no further simplifications possible. The final answer is $\frac{2}{81 \times x^4}$ .

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