# Rewrite each expression so that each term is in the form kx^{n}, where k is a real number, x is a positive real number, and n is a rational number. a)x^{-frac{2}{3}} times x^{frac{1}{3}}=? b) frac{10x^{frac{1}{3}}}{2x^{2}}=? c) (3x^{frac{1}{4}})^{-2}=?

Rewrite each expression so that each term is in the form $k{x}^{n},$ where k is a real number, x is a positive real number, and n is a rational number.
a)
b) $\frac{10{x}^{\frac{1}{3}}}{2{x}^{2}}=?$
c) $\left(3{x}^{\frac{1}{4}}{\right)}^{-2}=?$
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Step 1
We have to rewrite the given expression in the form of $k{x}^{n}.$
Before going to simplify expression, first we need to know about rule of exponents.
1.
2.
3.
Now, we will rewrite the given expression.
(a) Expression is
Given expression can be written as:

$={x}^{-\frac{1}{3}}$
(b) Expression is $\frac{10{x}^{\frac{1}{3}}}{2{x}^{2}}.$
Given expression can be written as:

$=5{x}^{-\frac{5}{3}}$
(c) Expression is $\left(3{x}^{\frac{1}{4}}{\right)}^{-2}$
Given expression can be written as:

$=3{x}^{-\frac{1}{2}}$