### Home > INT2 > Chapter 7 > Lesson 7.2.2 > Problem7-93

7-93.

Evaluate the expression below when $x=27$ and $y=16$.

$6x^{2/3}y^{1/4}\cdot x^{-1}y^{1/2}$

Start by simplifying the expression.
Remember that when you multiply numbers with the same base,  you can add the exponents together.

$6\left(x^{^{\frac{2}3{}}}x^{-1}\right)\left(y^{\frac{1}{4}}y^{\frac{1}{2}}\right)$

$6\left(x^{\frac{2}{3}-1}\right)\left(y^{\frac{1}{4}+\frac{1}{2}}\right)$

$6x^{-\frac{1}{3}}y^{\frac{3}{4}}$

Substitute the given values for $x$ and $y$ then simplify.
Fractional exponents represent a power and a root.
The root is determined by the denominator, and the power by the numerator.
For example, the exponent for $16$ means the $4$th root of $16$ raised to the $3$rd power.

$6\left(27^{-\frac{1}{3}}\right)\left(16^{\frac{3}{4}}\right)$

$6\left(\frac{1}{3}\right)(8)$

$16$