Hi, Braydon ! Long time no see. Hope it's all good with you.
First of all, that " -1 " exponent outside the whole thing. That means
invert everything inside. So you're really simplifying:
-21 y⁶ z⁻⁸ / 147 y⁴ z⁴
You can easily write this as the product of 3 separate fractions.
That doesn't change anything, but it makes it a lot easier to handle:
(-21/147) x (y⁶/y⁴) x (z⁻⁸/z⁴) .
Simplify each one, then just multiply them together again.
First one: (-21/147) Divide top and bottom by 21, and it's (-1/7) .
Second one: (y⁶/y⁴) Divide top and bottom by y⁴, and it's (y²) .
Third one: (z⁻⁸/z⁴) Multiply top and bottom by z⁸, and it's (1/z¹²).
Multiply them:
(-1/7) x (y²) x (1/z¹²) =
- y² / 7 z¹² .
That's exactly the same thing as the original expression in the picture,
but it's a lot prettier.