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Chapter 0: Problem 94

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

Short Answer

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

Step by step solution

01

Simplify Numerical Constants

First, simplify the numerical constants 72 and 9 by dividing 72 by 9 to get 8. The expression now should read - \(8 x^{\frac{3}{4}}/x^{\frac{1}{3}}\)
02

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 \(8x^{\frac{5}{12}}\)

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Most popular questions from this chapter

Evaluate each exponential expression in $$\frac{x^{14}}{x^{-7}}$$

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