# Math Help - Exponents

1. ## Exponents

(2t^3/5t^-4)^-2 I need help in this problem

It asks to simplify the exponent but the catch is the answer must be positive exponents ant help will be appreciated greatly

2. Originally Posted by Gomaz23
(2t^3/5t^-4)^-2 I need help in this problem

It asks to simplify the exponent but the catch is the answer must be positive exponents ant help will be appreciated greatly
$
(\frac {2t^3}{5t^{-4}})^{-2} = (\frac{2t^7}{5})^{-2} = \frac {5^2}{2^2t^{14}} = \frac {25}{4t^{14}}
$

3. Can you explain further. thnks tho

4. what part is troubling you?

$t^{-2} = \frac{1}{t^2}$

do you understand now?

5. howd you get 2sqrd

6. Originally Posted by Gomaz23
(2t^3/5t^-4)^-2 I need help in this problem

It asks to simplify the exponent but the catch is the answer must be positive exponents ant help will be appreciated greatly
Hi Gomaz23,

Here's another approach

$\left(\frac{2t^3}{5t^{-4}}\right)^{-2}=\left(\frac{5t^{-4}}{2t^3}\right)^2=\frac{25t^{-8}}{4t^6}=\frac{25t^{-14}}{4}=\frac{25}{4t^{14}}$

7. $
\left( \frac{2t^7}{5} \right)^{-2} = \left( \left( \frac{2t^7}{5} \right)^{-1} \right)^2 = \left( \frac{5}{2t^7} \right)^2 = \frac{5^2}{2^2 \cdot t^{7\cdot2}}
$

8. Originally Posted by metlx
what part is troubling you?

$t^{-2} = \frac{1}{t^2}$

do you understand now?
Originally Posted by Gomaz23
howd you get 2sqrd
It was posted as an example to try and help you see where the positive power has come from.

You are expected to know the rule $t^{-n} = \frac{1}{t^n}$. In your problem n = 14.

Note: If you expect to get additional help then you need to be specific in what you don't understand. Making some general comment that amounts to "I don't get it" is less than helpful in knowing what further help you need.

You might benefit from going back and reviewing the index laws you have learned so far.