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((2)/(3))^(-4)÷((6)/(4))^(-2)

$\left(\frac{2}{3}\right)^{-4} \div\left(\frac{6}{4}\right)^{-2}$

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Multiplication with rational exponents

Full solution

Q.

\left(\frac{2}{3}\right)^{-4} \div\left(\frac{6}{4}\right)^{-2}

Rewrite with Negative Exponents: Step $1$ : Rewrite the expression using the property of negative exponents, which states that $a^{-n} = \frac{1}{a^n}$ . $\left(\frac{2}{3}\right)^{-4}$ becomes $\frac{1}{\left(\frac{2}{3}\right)^4}$ and $\left(\frac{6}{4}\right)^{-2}$ becomes $\frac{1}{\left(\frac{6}{4}\right)^2}$ .
Calculate Powers: Step $2$ : Calculate the powers in the denominators. $\newline$ $(\frac{2}{3})^4 = (\frac{2^4}{3^4}) = \frac{16}{81}$ and $(\frac{6}{4})^2 = (\frac{6^2}{4^2}) = \frac{36}{16}$ .
Substitute Back: Step $3$ : Substitute back into the original expression. $\newline$ $\frac{1}{\frac{16}{81}}$ ÷ $\frac{1}{\frac{36}{16}}$ = $\frac{81}{16}$ ÷ $\frac{16}{36}$ .
Simplify Division: Step $4$ : Simplify the division of fractions by multiplying by the reciprocal. $\newline$ $(\frac{81}{16}) \times (\frac{36}{16}) = \frac{81\times36}{16\times16} = \frac{2916}{256}$ .

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