Question

Simplify this expression. Assume that y and z are both nonzero.

Answer 1

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.