# Thread: Simplify equation with steps

1. ## Simplify equation with steps

(64n^9)^2/3

(5b^2c^1/4)^3

2. ## Re: Simplify equation with steps

Originally Posted by jobbles85
(64n^9)^2/3

(5b^2c^1/4)^3
Not showing steps, that's your job.

You need to use the following index laws:

\displaystyle \displaystyle \begin{align*} \left(a^m\right)^p &= a^{m \cdot p} \\ \\ \left(a \cdot b\right)^n &= a^n \cdot b^n \end{align*}

3. ## Re: Simplify equation with steps

Originally Posted by Prove It
Not showing steps, that's your job.

You need to use the following index laws:

\displaystyle \displaystyle \begin{align*} \left(a^m\right)^p &= a^{m \cdot p} \\ \\ \left(a \cdot b\right)^n &= a^n \cdot b^n \end{align*}
so would the steps be..
=64n9x2/3
=64n^6

4. ## Re: Simplify equation with steps

Originally Posted by jobbles85
so would the steps be..
=64n9x2/3
=64n^6
correction ...

$\displaystyle (64n^9)^{\frac{2}{3}} = 64^{\frac{2}{3}}n^6$

finish by simplifying the factor $\displaystyle 64^{\frac{2}{3}}$ ...

5. ## Re: Simplify equation with steps

(64n^9)^2/3
=642/3n^6
=(3√64^2)(n^6)
=(3√4096)(n^6)
=±16n^6

God I have no clue what I'm doing

(5b^2c^1/4)^3
=(5)^3 (b^2)^3 (c^1/4)^3
=125b^5c^3/4

6. ## Re: Simplify equation with steps

would have been really easy if you knew that $\displaystyle 64 = 4^3$ ... and it's not $\displaystyle \pm$

last one is correct