Problem 94 - College Algebra

Question

Simplify using properties of exponents. $$\frac{72 x^{\frac{3}{4}}}{9 x^{\frac{1}{3}}}$$

Step-by-Step Solution

Answer

The simplified form of the given expression is \(8x^{\frac{5}{12}}\)

Step 1: Simplify Numerical Constants

First, simplify the numerical constants 72 and 9 by dividing 72 by 9 to get 8. The expression now should read - \(8 x^{\frac{3}{4}}/x^{\frac{1}{3}}\)

Step 2: Apply laws of exponents

Using the law of division for exponents, subtract the lower exponent fraction from the higher exponent fraction. That is \(\frac{3}{4} - \frac{1}{3}\) which is equivalent to \(\frac{9 - 4}{12} = \frac{5}{12}\). Therefore, now the expression reads as \(8x^{\frac{5}{12}}\)