1. ## Simplify expression

6y^-2(2y^4)^-3

2. ## Re: Simplify expression

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

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

$\displaystyle x^{-a}=\frac{1}{x^a}$

$\displaystyle (x^a)^b=x^{ab}$

3. ## Re: Simplify expression

Originally Posted by Dobby
6y^-2(2y^4)^-3
$\displaystyle 6y^{-2} \cdot (2y^4)^{-3}=\frac{6}{y^2} \cdot \frac{1}{(2y^4)^3}=\frac{6}{y^2} \cdot \frac {1}{2^3 \cdot (y^4)^3}=$

$\displaystyle = \frac{6}{y^2} \cdot \frac{1}{8 \cdot y^{12}}=\frac{3}{4}\cdot \frac{1}{y^{16}}=\frac{3}{4} \cdot y^{-16}$

4. ## Re: Simplify expression

Originally Posted by princeps
$\displaystyle 6y^{-2} \cdot (2y^4)^{-3}=\frac{6}{y^2} \cdot \frac{1}{(2y^4)^3}=\frac{6}{y^2} \cdot \frac {1}{2^3 \cdot (y^4)^3}=$

$\displaystyle = \frac{6}{y^2} \cdot \frac{1}{8 \cdot y^{12}}=\frac{3}{4}\cdot \frac{1}{y^{16}}=\frac{3}{4} \cdot y^{-16}$
Correct

5. ## Re: Simplify expression

[QUOTE=princeps;710102]$\displaystyle 6y^{-2} \cdot (2y^4)^{-3}=\frac{6}{y^2} \cdot \frac{1}{(2y^4)^3}=\frac{6}{y^2} \cdot \frac {1}{2^3 \cdot (y^4)^3}=$

$\displaystyle = \frac{6}{y^2} \cdot \frac{1}{8 \cdot y^{12}}=\frac{3}{4}\cdot \frac{1}{y^{16}}=\frac{3}{4} \cdot y^{-16}$[/QUOTE

typo error