Laws of Exponents II: Simplify Expression

[reenmachine]

Homework Statement

Simplify this expression and express the result with only positive exponants.

Homework Equations

The expression:

$\left( \frac {(-49^4 \ c^{-2} \ d)^3}{14^6 \ c^{-1} \ d^2} \right)^{-1}$

The Attempt at a Solution

$\left( \frac {(-49^4 \ c^{-2} \ d)^3}{14^6 \ c^{-1} \ d^2} \right)^{-1}$

$\left( \frac {(-(7^2)^4 \ c^{-2} \ d)^3}{(2 \cdot 7)^6 \ c^{-1} \ d^2} \right)^{-1}$

$\left( \frac {(- 7^8 \ c^{-2} \ d)^3}{2^6 \cdot 7^6 \ c^{-1} \ d^2} \right)^{-1}$

$\left( \frac {- 7^{24} \ c^{-6} \ d^3}{2^6 \cdot 7^6 \ c^{-1} \ d^2} \right)^{-1}$

$\left( \frac {- 7^{18} \ c^{-5} \ d}{2^6} \right)^{-1}$

$\left( \frac {- 7^{-18} \ c^5 \ d^{-1}}{2^{-6}} \right)$

$\left( \frac {- 2^6 \ c^5}{7^{18} \ d} \right)$

Is this correct?

Thank you!

 

[jedishrfu]

Yes that seems correct.

I did it a bit differently though by going outside into eliminate the outermost -1 exponent:

(A/B)^-1 = B/A

and then I moved factors to the numerator or denominator to eliminate the - exponent then I simplified things

to get what you got.

 

[reenmachine]

thank you!