Question

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

Answer 1

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.

Answer 2

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

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