# Thread: Need Help Exponents

1. ## Need Help Exponents

I need to write these in exponential form and use exponent laws to simplify and evaluate any help would be appreciated

$
\sqrt{1000} X \sqrt[3]{1000} / \sqrt[6]{1000}
$

2. Hello, TH1;98010!

Simplify and evaluate: . $\frac{
\sqrt{1000}\cdot\sqrt[3]{1000}}{\sqrt[6]{1000}}$
Write in exponential form:

. . $\frac{(10^3)^{\frac{1}{2}}\cdot(10^3)^{\frac{1}{3} }}{(10^3)^{\frac{1}{6}}} \;=\;\frac{10^{\frac{3}{2}}\cdot10^1}{10^{\frac{1} {2}}} \;= \;10^{(\frac{3}{2}+1-\frac{1}{2})} \;=\;10^2\;=\;100$

3. Thanks for the help I have a couple more since I couldnt work out the code

$
\left( \sqrt{64} \right)^2 / \sqrt[3]{64}
$

$
4+4^1 / 4-4{^1}
$

For the second question the exponents are negative both of them

$
\sqrt{4^3}(\sqrt[5]{4^4}) / \sqrt{2^10}
$

4. Hello,TH1!

$\frac{\left( \sqrt{64} \right)^2}{\sqrt[3]{64}}$

We have: . $\frac{(64^{\frac{1}{2}})^2}{64^{\frac{1}{3}}} \;=\;\frac{64^1}{64^{\frac{1}{3}}} \;=\;64^{(1-\frac{1}{3})} \;=\;64^{\frac{2}{3}}\;=\;(\sqrt[3]{64})^2 \;=\;4^2\;=\;16$

$\frac{4+4^{-1}}{4-4^{-1}}$
Multiply by $\frac{4}{4}\!:\;\;\frac{4}{4}\cdot\frac{4 + 4^{-1}}{4 - 4^{-1}} \;=\;\frac{16+1}{16-1} \;=\; \frac{17}{15}$

$\frac{\sqrt{4^3}\cdot\sqrt[5]{4^4}}{\sqrt{2^{10}}}$
Change all the bases to 2s.

$\frac{\sqrt{(2^2)^3}\cdot\sqrt[5]{(2^2)^4} }{\sqrt{2^{10}}} \;=\;\frac{(2^6)^{\frac{1}{2}} (2^8)^{\frac{1}{5}}} {(2^{10})^{\frac{1}{2}}} \;=\;\frac{2^3\cdot2^{\frac{8}{5}}}{2^5} \;=\;2^{(3+\frac{8}{5}-5)} \;=\;2^{-\frac{2}{5}}$