Question

I have been stuck on number 10 (this problem) for a while now. Can anyone help me with it and walk me through every step in order to get a correct answer for the math problem in the picture? Thanks!! I’ll be giving away as many points as I can for a response! It must follow the criteria listed above though. Help and steps.

Answer 1

When you multiply a same number but with different powers, you can simply add the powers together. So, in your question, add the powers -1 and -7 together.
7^(-1) x 7^(-7) = 7^(-8)

When you divide a same number but with different powers, you subtract the power at the top with the power from the denominator. So, -8 - (-7) = -1.
7^(-8) / 7^(-7) = 7^(-1)

So your answer would be 7^(-1).
Hopefully my explanation was clear?

Answer 2

You know that a number divided by itself is 1, so this is

$\dfrac{7^{-1}\times 7^{-7}}{7^{-7}}=7^{-1}\times\left(\dfrac{7^{-7}}{7^{-7}}\right)\\\\=7^{-1}\times 1=7^{-1}=\bf{\dfrac{1}{7}}$

Something to a negative power is the reciprocal of that thing to the opposite positive power.