### Home > CCA > Chapter 11 > Lesson 11.3.1 > Problem11-76

11-76.

Evaluate the expression below when x = 27 and y = 16. Homework Help ✎

6x2/3y1/4 · x1y1/2

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 4th root of 16 raised to the 3rd power.

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

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

16