Question #1c5a0

Question

Question #1c5a0

1 Answer

Impact of this question

1109 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-24T17:57:32

$= \sqrt[24]{a^{7} b^{13}}$ $=root24(a^7b^13)$

Explanation:

Let's write the roots as indices.

$\frac{\sqrt[8]{a^{5} b^{7}}}{\sqrt[3]{a b}} = \frac{a^{\frac{5}{8}} b^{\frac{7}{8}}}{a^{\frac{1}{3}} b^{\frac{1}{3}}}$ $(root8(a^5b^7))/(root3(ab)) = (a^(5/8)b^(7/8))/(a^(1/3)b^(1/3)$

When dividing, subtract the indices of like bases.

$a^{\frac{5}{8} - \frac{1}{3}} \times b^{\frac{7}{8} - \frac{1}{3}}$ $a^(5/8-1/3) xx b^(7/8-1/3)$

$= a^{\frac{15 - 8}{24}} \times b^{\frac{21 - 8}{24}}$ $= a^((15-8)/24) xx b^((21-8)/24)$

$= a^{\frac{7}{24}} \times b^{\frac{13}{24}}$ $= a^(7/24) xxb^(13/24)$

$= \sqrt[24]{a^{7} b^{13}}$ $=root24(a^7b^13)$

Science

Math

Humanities

... and beyond

Question #1c5a0

1 Answer

Explanation:

Related questions

Impact of this question