MHB Simplifying exponential expressions

[arl2267]

Simplify 8p^-3 x (4p²)^-2/p-5.

This is what I got:

First thing I did was flip everything to get rid of the negative exponents:

p⁵/8p³x(4p²)²

next thing I did was multiply the 4p² by 2

p⁵/ 8p³x16p⁴Then I subtracted thep⁵ from the 8p³

p²/8x16p⁴

and ended up with

1/128p² I know that the answer is 1/2p²​ so where did I go wrong?

 

[pickslides]

After expanding the brackets

$\displaystyle \frac{8p^{-3}\times 4^{-2}\times p^{-4}}{p^{-5}}$

$\displaystyle \frac{8p^{-3}\times p^{-4}}{4^{2}\times p^{-5}}$

You can now see the numerical part is $\displaystyle\frac{8}{16}= \frac{1}{2}$

 

[MarkFL]

In your first step where you "flip" everything, you cannot do this with the 8 since it does not have a negative exponent. If you had left the 8 in the numerator, then you would have gotten the desired result.

edit: Welcome to the forum, and I certainly appreciate the fact that you show your work...this makes it much easier to address where your error(s) may be.