Divide Monomials: example 10.56

Simplify: ${(\frac{2 x^{3}}{3 y})}^{4} .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Simplify: ${(\frac{5 b}{9 c^{3}})}^{2} .$

How did it go?

	${(\frac{2 x^{3}}{3 y})}^{4}$
Raise the numerator and denominator to the fourth power using the Quotient to a Power Property.	$\frac{{(2 x^{3})}^{4}}{{(3 y)}^{4}}$
Raise each factor to the fourth power, using the Power to a Power Property.	$\frac{2^{4} {(x^{3})}^{4}}{3^{4} y^{4}}$
Use the Power Property and simplify.	$\frac{16 x^{12}}{81 y^{4}}$

	${(\frac{2 x^{3}}{3 y})}^{4}$
Raise the numerator and denominator to the fourth power using the Quotient to a Power Property.	$\frac{{(2 x^{3})}^{4}}{{(3 y)}^{4}}$
Raise each factor to the fourth power, using the Power to a Power Property.	$\frac{2^{4} {(x^{3})}^{4}}{3^{4} y^{4}}$
Use the Power Property and simplify.	$\frac{16 x^{12}}{81 y^{4}}$