Question

simplify 64/125 raised to the power-2/3

Answer 1

Answer:

$\left(\frac{64}{125}\right)^{\frac{-2}{3}}=\frac{25}{16}$

Step-by-step explanation:

$Given,\left(\frac{64}{125}\right)^{\frac{-2}{3}}$

$=\left(\frac{4^{3}}{5^{3}}\right)^{\frac{-2}{3}}$

$=\left(\big(\frac{4}{5}\big)^{3}\right)^{\frac{-2}{3}}$

/* By Exponential Law:

$\frac{a^{n}}{b^{n}}=\left(\frac{a}{b}\right)^{n}$

$=\left(\frac{4}{5}\right)^{3\times \frac{-2}{3}}$

$=\left(\frac{4}{5}\right)^{-2}$

\* By Exponential Law:

$\left(a^{m}\right)^{n}=a^{mn}$

$=\left(\frac{5}{4}\right)^{2}$

/* By Exponential Law:

$\left(\frac{a}{b}\right)^{-n}=\left(\frac{b}{a}\right)^{n}$

$=\frac{5^{2}}{4^{2}}\\=\frac{25}{16}$

Therefore,

$\left(\frac{64}{125}\right)^{\frac{-2}{3}}=\frac{25}{16}$

•••♪

Answer 2

Answer:

25/16

Step-by-step explanation:

64/125^-2/3=

125/64^2/3=

(5^3/4^3)^2/3=

(5/4)^2=

25/16