Question

# How do you multiply and simplify (\frac { y ^ { - 3} } { z ^ { 3} } ) ( - 2x ^ { 3} y ^ { 2} z ) ^ { - 3}?

How do you multiply and simplify (\frac { y ^ { - 3} } { z ^ { 3} } ) ( - 2x ^ { 3} y ^ { 2} z ) ^ { - 3}?

Answer 1

(1)/(-8  x^9  y^9  z^6)

#### Explanation:

This problem isn't hard, but it is painstaking.

Solving it correctly depends on knowing that you can get rid of negative exponents by flipping them to the other side of the fraction bar and making them positive.

Simplify

((y^(−3))/(z^3))(−2 x^3 y^2 z)^(−3)

1) Get rid of the minus signs on the exponents in the numerator by flipping them to the denominator and reversing their signs

(1)/(y^3 z^3)xx(1)/(−2  x^3  y^2  z)^(3)

2) Raise all the powers inside the parentheses to the power of 3 outside the parentheses.
To raise a power to a power, multiply

After you have multiplied all the exponents by 3, you will get this:

(1)/(y^3  z^3)xx(1)/(−2^3  x^9  y^6  z^3

3) This is just one long multiplication problem

(1)/(-2^3 y^3  z^3  x^9  y^6  z^3)

So therefore you can rearrange the bases for your convenience

3) Group like bases

(1)/(-2^3  x^9   (y^3)(y^6)  (z^3)(z^3)

4) Multiply like bases
To multiply exponents, you add them

(1)/(-2^3 x^9 y^9 z^6) $\leftarrow$ answer

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