# Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers. a) r^{^1/_6} r^{^5/_6} b) a^{^3/_5} a^{^3/_{10}}

Simplify the expression and express the answer using rational exponents. Assume that all letters denote positive numbers.
a)
b)
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Jaylen Fountain

a) ${a}^{\frac{m}{n}}=\left(\sqrt[n]{a}{\right)}^{m}=\sqrt[n]{{a}^{m}}$
The exponent ${}^{m}{/}_{n}$ consists of two parts:
The denominator n is the root and the numerator m is the export
Exponent Rule:
${a}^{{-}^{m}{/}_{n}}=\frac{1}{{a}^{{}^{m}{/}_{n}}}$
Calculation:

Apply exponent rule simplify the expression,

$={r}^{\frac{6}{6}}$

Final statement (a):

b) ${a}^{\frac{m}{n}}=\left(\sqrt[n]{a}{\right)}^{m}=\sqrt[n]{{a}^{m}}$
The exponent m//n consists of two parts:
The denominator n is the root and the numerator m is the export
Exponent Rule:
${a}^{{-}^{m}{/}_{n}}=\frac{1}{{a}^{{}^{m}{/}_{n}}}$
Calculation:

Apply exponent rule in we get,

Final statement (b):