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

Identify base and exponent: Identify the base and the exponent in (3x)^(-4). 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) = 1/(a^n). So, (3x)^(-4) becomes 1/((3x)^4).Multiply by reciprocal: Multiply the fraction (2) by the reciprocal of (3x)^(-4). This gives us 2 * (1/((3x)^4)).Simplify expression by multiplication: Simplify the expression by multiplying the numerators and denominators. This results in 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 2/(3^4 * x^4).Calculate 3^4: Calculate 3^4 to simplify the denominator further. 3^4 equals 81.Substitute 81 in denominator: Substitute 81 for 3^4 in the denominator. This gives us 2/(81 * x^4).Final simplified answer: The expression is now fully simplified, and there are no further simplifications possible. The final answer is 2/(81 * x^4).

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

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Algebra 2

Evaluate rational exponents

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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 $\frac{2}{81 \times x^4}$ .