Question #2ffc4

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Question #2ffc4

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Answer 1 · 2016-01-07T15:35:15

$25^{\frac{3}{4}} = 5 \cdot \sqrt[4]{5^{2}}$ $25^(3/4)=5*root(4)(5^2)$

Explanation:

The properties of Exponents tell us that:

$a^{\frac{n}{m}} = \sqrt[m]{a^{n}}$ $a^(n/m)=root(m)(a^n)$

and

${(a^{p})}^{q} = a^{p \cdot q}$ $(a^p)^q=a^(p*q)$

and

$a^{h} \cdot a^{k} = a^{h + k}$ $a^h*a^k=a^(h+k)$

then:

$25^{\frac{3}{4}} = \sqrt[4]{25^{3}} = \sqrt[4]{{(5^{2})}^{3}} = \sqrt[4]{5^{6}} =$ $25^(3/4)=root(4)(25^3)=root(4)((5^2)^3)=root(4)(5^6)=$
$= \sqrt[4]{5^{4} \cdot 5^{2}} = \sqrt[4]{5^{4}} \cdot \sqrt[4]{5^{2}} = 5 \sqrt[4]{5^{2}}$ $=root(4)(5^4*5^2)=root(4)(5^4)*root(4)(5^2)=5root(4)(5^2)$

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Question #2ffc4

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