Question

Divide cube root of 128 by fifth root of 64

Answer 1

Answer:

Please find the attached image.

Step-by-step explanation:

Answer 2

$\dfrac{\sqrt[3]{128}}{\sqrt[5]{64}}=\sqrt[15]{131072}$

Step-by-step explanation:

Given : Expression cube root of 128 by fifth root of 64.

To find : Divide the expression ?

Solution :

Writing the expression as,

$\dfrac{\sqrt[3]{128}}{\sqrt[5]{64}}$

First we factories the numbers,

$\dfrac{\sqrt[3]{128}}{\sqrt[5]{64}}=\dfrac{\sqrt[3]{2\times 2\times 2\times 2\times 2\times 2\times 2}}{\sqrt[5]{2\times 2\times 2\times 2\times 2\times 2}}$

$\dfrac{\sqrt[3]{128}}{\sqrt[5]{64}}=\dfrac{\sqrt[3]{2^3\times 2^3\times 2}}{\sqrt[5]{2^5\times 2}}$

$\dfrac{\sqrt[3]{128}}{\sqrt[5]{64}}=\dfrac{2\times 2\sqrt[3]{2}}{2\sqrt[5]{2}}$

$\dfrac{\sqrt[3]{128}}{\sqrt[5]{64}}=\dfrac{2(2)^{\frac{1}{3}}}{(2)^{\frac{1}{5}}}$

$\dfrac{\sqrt[3]{128}}{\sqrt[5]{64}}=\dfrac{(2)^{\frac{4}{3}}}{(2)^{\frac{1}{5}}}$

$\dfrac{\sqrt[3]{128}}{\sqrt[5]{64}}=(2)^{\frac{4}{3}-\frac{1}{5}}$

$\dfrac{\sqrt[3]{128}}{\sqrt[5]{64}}=(2)^{\frac{20-3}{15}}$

$\dfrac{\sqrt[3]{128}}{\sqrt[5]{64}}=(2)^{\frac{17}{15}}$

Therefore, $\dfrac{\sqrt[3]{128}}{\sqrt[5]{64}}=\sqrt[15]{131072}$

#Learn more

Divide the squer root of 64 by the cube of 2

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