# Thread: Perform the indicated operations and simplify equation completely.

1. ## Perform the indicated operations and simplify equation completely.

I have a couple of problems I haven't been able to work out correctly...

1.
I am confused because of the negative exponents in this problem:

t^-6 (2t)^3
------------
t^3

2.
(x^4 + 4x^2 - 5x + 3) - (2x - 5)^2

If anyone could help me with these asap, that would be great! Thanks.

2. Originally Posted by rckstr4lfe
I have a couple of problems I haven't been able to work out correctly...

1.
I am confused because of the negative exponents in this problem:

t^-6 (2t)^3
------------
t^3

2.
(x^4 + 4x^2 - 5x + 3) - (2x - 5)^2

If anyone could help me with these asap, that would be great! Thanks.
to #1:

Use the laws of powers:

$\displaystyle \dfrac{t^{-6} \cdot (2t)^3}{t^3} = 8t^{-6+3-3}=8t^{-6} = \dfrac8{t^{6}}=\left(\dfrac2{t^2}\right)^3$

to #2:
Expand the brackets and collect like terms:

$\displaystyle (x^4 + 4x^2 - 5x + 3) - (2x - 5)^2 = x^4+4x^2-5x+3-4x^2+20x-25 = x^4+15x-22$