# Thread: Simplifying some algebraic exponent expressions

1. ## Simplifying some algebraic exponent expressions

Question 1:

$\frac{\sqrt[10]{1024x^{20}}}{\sqrt[9]{512x^{27}}}$

$=\frac{1024x^{\frac{20}{10}}}{512x^{\frac{27}{9}}}$

$=\frac{1024x^{\frac{2}{1}}}{512x^{\frac{3}{1}}}$

$=2x^{-1}$

$=\frac{2}{x}$

$\frac{1}{x}$

Question 2:

$\frac{\sqrt[6]{(8x^{6})^2}}{\sqrt[4]{625x^{8}}}$

$=\frac{\sqrt[6]{64x^{12}}}{\sqrt[4]{625x^{8}}}$

$=\frac{64x^{\frac{12}{6}}}{625x^{\frac{8}{4}}}$

$=\frac{64}{625}$

$\frac{2}{5}$

Does anyone know where I made the errors?

2. Originally Posted by RogueDemon
Question 1:

$\frac{\sqrt[10]{1024x^{20}}}{\sqrt[9]{512x^{27}}}$

$=\frac{1024x^{\frac{20}{10}}}{512x^{\frac{27}{9}}}$

$=\frac{1024x^{\frac{2}{1}}}{512x^{\frac{3}{1}}}$

$=2x^{-1}$

$=\frac{2}{x}$

$\frac{1}{x}$

Question 2:

$\frac{\sqrt[6]{(8x^{6})^2}}{\sqrt[4]{625x^{8}}}$

$=\frac{\sqrt[6]{64x^{12}}}{\sqrt[4]{625x^{8}}}$

$=\frac{64x^{\frac{12}{6}}}{625x^{\frac{8}{4}}}$

$=\frac{64}{625}$

$\frac{2}{5}$

Does anyone know where I made the errors?
1.

$\frac{\sqrt[10]{1024x^{20}}}{\sqrt[9]{512x^{27}}}$

$= \frac{1024^{\frac{1}{10}}x^{\frac{20}{10}}}{512^{\ frac{1}{9}}x^{\frac{27}{9}}}$

$= \frac{(2^{10})^{\frac{1}{10}}x^{\frac{20}{10}}}{(2 ^9)^{\frac{1}{9}}x^{\frac{27}{9}}}$

$= \frac{2x^2}{2x^3}$

$= \frac{x^2}{x^3}$

Do the same for the second problem

3. ## simplifying expressions

Originally Posted by RogueDemon
Question 1:

$\frac{\sqrt[10]{1024x^{20}}}{\sqrt[9]{512x^{27}}}$

$=\frac{1024x^{\frac{20}{10}}}{512x^{\frac{27}{9}}}$

$=\frac{1024x^{\frac{2}{1}}}{512x^{\frac{3}{1}}}$

$=2x^{-1}$

$=\frac{2}{x}$

$\frac{1}{x}$

Question 2:

$\frac{\sqrt[6]{(8x^{6})^2}}{\sqrt[4]{625x^{8}}}$

$=\frac{\sqrt[6]{64x^{12}}}{\sqrt[4]{625x^{8}}}$

$=\frac{64x^{\frac{12}{6}}}{625x^{\frac{8}{4}}}$

$=\frac{64}{625}$

$\frac{2}{5}$