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polet [3.4K]
3 years ago
13

Please helppp (750/512)^1/3 what is equivilant to this??

Mathematics
2 answers:
marysya [2.9K]3 years ago
8 0

Answer:

\frac{5\sqrt[3]{6}}{8}

Step-by-step explanation:

We have been given an exponential number. We are supposed to simplify our given number.

(\frac{750}{512})^{\frac{1}{3}  

Using fractional exponent rule x^\frac{m}{n}=\sqrt[n]{x^m}, w ecan write our given number as:

(\frac{750}{512})^{\frac{1}{3}}=\sqrt[3]{(\frac{750}{512})^1}

(\frac{750}{512})^{\frac{1}{3}}=\sqrt[3]{\frac{750}{512}}

We can rewrite 512 as 8^3 and 750 as 125*6.

(\frac{750}{512})^{\frac{1}{3}}=\sqrt[3]{\frac{125*6}{8^3}}

We can rewrite 125 as 5^3

(\frac{750}{512})^{\frac{1}{3}}=\sqrt[3]{\frac{5^3*6}{8^3}}

Using radical rule \sqrt[n]{a^n}=a, we will get:

(\frac{750}{512})^{\frac{1}{3}}=\frac{5\sqrt[3]{6}}{8}

Therefore, \frac{5\sqrt[3]{6}}{8} is equivalent to our given number.

Misha Larkins [42]3 years ago
6 0
\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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