Help me with Alg.1 !Thankssssssss?

Question

Simplify:

4y^5z^2/8yz^9

(5d^3e^2f/d^-2e^6f^2)^-3

Please help me explain how you get it!

Answer 1

4y^5 z^2 / 8y z^9

To divide y^5 by y, subtact the power [1] in the denominator from that [5] in the numerator. Result y^4 ...(1)

Dividing 4 into 8 gives 2, making 4 / 8 = 1 / 2 ...(2)

z^2 / z^9 = 1 / z^(9 - 2) ...(2)

= 1 / z^7 ...(3)

Multiply together (1), (2) and (3) to get:

y^4 / (2z^7).

(5d^3 e^2f /d^-2 e^6 f^2)^-3

d^3 / d^(- 2) = d^(3 - (- 2)) = d^5.

e^2 / e^6 = e^(2 - 6) = e^(- 4) = 1 / e^4.

f / f^2 = 1 / f^(2 - 1) = 1 / f.

Multiplying all these together and the 5 gives:

5 d^5 / (e^4 f)

Raising the whole fraction to power - 3 inverts it and multiplies all the indices by 3, giving:

e^12 f^3 / (5^3 d^15)

= e^12 f^3 / (125 d^15).