Question

Please helppp

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

Answer 1

`\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)^{(1)/(3)}\implies \cfrac{750^{(1)/(3)}}{512^{(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}`

Answer 2

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

Explanation:

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

`((750)/(512))^{(1)/(3)`

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

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

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

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

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

We can rewrite 125 as
`5^3`

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

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

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

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