$\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad
\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\
-------------------------------$

$\bf \left( \cfrac{750}{512} \right)^{\frac{1}{3}}\implies \cfrac{750^{\frac{1}{3}}}{512^{\frac{1}{3}}}\implies \cfrac{\sqrt[3]{750^1}}{\sqrt[3]{512^1}}\quad 
\begin{cases}
750=2\cdot 3\cdot 5\cdot 5\cdot 5\\
\qquad 2\cdot 3\cdot 5^3\\
\qquad 6\cdot 5^3\\
512=8\cdot 8\cdot 8\\
\qquad 8^3
\end{cases}
\\\\\\
\cfrac{\sqrt[3]{750}}{\sqrt[3]{512}}\implies \cfrac{\sqrt[3]{6\cdot 5^3}}{\sqrt[3]{8^3}}\implies \cfrac{5\sqrt[3]{6}}{8}$

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3 years ago

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Which property would allow you to use mental computation to simplify the problem 23 + (7 + 9)?

katrin2010 [14]

Distributive property

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3 years ago