How do you write with fractional exponents $\frac{1}{5} ({\sqrt{x}}^{2})$ $1/5(sqrt x^2)$ ?

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Answer 1 · 2015-08-02T13:42:48

$\frac{1}{5} {(\sqrt{x})}^{2} = \frac{1}{5} x$ $color(red)( 1/5 (sqrtx)^2 = 1/5x)$

$\frac{1}{5} {(\sqrt{x})}^{2} = \frac{1}{5} {(x^{\frac{1}{2}})}^{2}$ $1/5 (sqrtx)^2 = 1/5 (x^(1/2))^2$

But ${(x^{a})}^{b} = x^{a b}$ $(x^a)^b = x^(ab)$ , so

${(x^{\frac{1}{2}})}^{2} = x^{\frac{2}{2}} = x^{1} = x$ $(x^(1/2))^2= x^(2/2) =x^1 = x$

∴ $\frac{1}{5} {(\sqrt{x})}^{2} = \frac{1}{5} x$ $1/5 (sqrtx)^2 = 1/5x$

How do you write with fractional exponents 15(√x2)1/5(sqrt x^2)?