Question

example 6 apply properties of exponents to rational exponents
simplify each expression.
a. $(3xy^{\frac{3}{2}})^0(x^2y)^{\frac{1}{2}}$
$(3xy^{\frac{3}{2}})^0(x^2y)^{\frac{1}{2}} = (1)(x^2y)^{\frac{1}{2}}$ zero exponent property
$= x^{2\cdot\frac{1}{2}}y^{\frac{1}{2}}$ power of a product
$= \underline{\quad\quad\quad}$ simplify.

Explanation:

Step1: Apply zero exponent property

$(3xy^{\frac{3}{2}})^0(x^2y)^{\frac{1}{2}} = (1)(x^2y)^{\frac{1}{2}}$

Step2: Apply power of a product

$= x^{2 \cdot \frac{1}{2}}y^{\frac{1}{2}}$

Step3: Simplify exponents

$= x^{1}y^{\frac{1}{2}}$

Answer:

$xy^{\frac{1}{2}}$