# Thread: Simplifying some algebraic exponent expressions

1. ## Simplifying some algebraic exponent expressions

Question 1:

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

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

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

$\displaystyle =2x^{-1}$

$\displaystyle =\frac{2}{x}$

Textbook answer:

$\displaystyle \frac{1}{x}$

Question 2:

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

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

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

$\displaystyle =\frac{64}{625}$

Textbook answer:

$\displaystyle \frac{2}{5}$

Does anyone know where I made the errors?

2. Originally Posted by RogueDemon
Question 1:

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

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

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

$\displaystyle =2x^{-1}$

$\displaystyle =\frac{2}{x}$

Textbook answer:

$\displaystyle \frac{1}{x}$

Question 2:

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

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

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

$\displaystyle =\frac{64}{625}$

Textbook answer:

$\displaystyle \frac{2}{5}$

Does anyone know where I made the errors?
1.

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

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

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

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

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

Do the same for the second problem

3. ## simplifying expressions

Originally Posted by RogueDemon
Question 1:

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

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

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

$\displaystyle =2x^{-1}$

$\displaystyle =\frac{2}{x}$

Textbook answer:

$\displaystyle \frac{1}{x}$

Question 2:

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

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

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

$\displaystyle =\frac{64}{625}$

Textbook answer:

$\displaystyle \frac{2}{5}$

Does anyone know where I made the errors?

in the first the numbers must show new exponents like 1024^1/10.when you make the corrections the answer is 1/x.Follow the same way in the second.

bjh