Question
Write $(625)^{-\frac{1}{4}}$ in decimal form.
✓
Answer
We have to write $(625)^{\frac{-1}{4}}$ in decimal form.
So, $(625)^{\frac{-1}{4}}=\frac{1}{625^{\frac{1}{4}}}$
$=\Big(\frac{1}{(5^4)}\Big)^{\frac{1}{4}}$
$(625^{\frac{-1}{4}})=\Big(\frac{1}{5}\Big)^{4\times\frac{1}{4}}$
$=\frac{1}{5}$
$=0.2$ Hence the decimal form of $(625)^{-\frac{1}{4}}$ is $0.2$
So, $(625)^{\frac{-1}{4}}=\frac{1}{625^{\frac{1}{4}}}$
$=\Big(\frac{1}{(5^4)}\Big)^{\frac{1}{4}}$
$(625^{\frac{-1}{4}})=\Big(\frac{1}{5}\Big)^{4\times\frac{1}{4}}$
$=\frac{1}{5}$
$=0.2$ Hence the decimal form of $(625)^{-\frac{1}{4}}$ is $0.2$
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