Question

for any two real numbers a and b where b ≠0 and for all integers is this true

Answer 1

Given:-

$64^{\frac{1}{4}},256^{\frac{1}{8}},125^{\frac{1}{3}}$

To find:-

The simplified value.

So now we have,

$\begin{gathered} 64=2\times2\times2\times2\times2\times2 \\ 256=2\times2\times2\times2\times2\times2\times2\times2 \\ 125=5\times5\times5 \end{gathered}$

So we have,

$64=2^6,256=2^8,125=5^3$

So now,

$\begin{gathered} 64^{\frac{1}{4}}=(2^6)^{\frac{1}{4}},256=(2^8)^{\frac{1}{8}},125=(5^3)^{\frac{1}{3}} \\ 64=4,256=2,125=5 \end{gathered}$

So the value is,

$4,6,5$