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Chapter 0: Problem 91

Simplify using properties of exponents. $$\left(7 x^{\frac{1}{3}}\right)\left(2 x^{\frac{1}{4}}\right)$$

Short Answer

Expert verified
The simplified form of \(\left(7 x^{\frac{1}{3}}\right)\left(2 x^{\frac{1}{4}}\right)\) is \(14x^{\frac{7}{12}}\).

Step by step solution

01

Multiply coefficients

Multiply the coefficients. We have 7 and 2 as coefficients. Multiply them and write down the result. So, \(7 \times 2 = 14.\)
02

Use properties of exponent

Apply the rule for when the bases are the same and we are multiplying: we add the exponents. So, \(x^{\frac{1}{3}} \times x^{\frac{1}{4}}\) becomes \(x^{\frac{1}{3} + \frac{1}{4}}.\)
03

Simplifying the exponent

Simplify the exponent by calculating the sum \(\frac{1}{3} + \frac{1}{4}\). Find a common denominator of 3 and 4, which is 12, and do the addition. The simplification results in \(\frac{7}{12}\).
04

Write the final simplified expression

Combine the results of step 1 and step 3 to obtain the final simplified expression. The coefficient 14 (from step 1) is multiplied with the base x raised to the power \(\frac{7}{12}\) (from step 3). Our final result is \(14x^{\frac{7}{12}}\).

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Most popular questions from this chapter

Exercises will help you prepare for the material covered in the next section. Evaluate each exponential expression in $$ \frac{x^{30}}{x^{-10}} $$

Exercises \(142-144\) will help you prepare for the material covered in the next section. Simplify and express the answer in descending powers of \(x\) : $$2 x\left(x^{2}+4 x+5\right)+3\left(x^{2}+4 x+5\right)$$

What does \(a^{\frac{m}{n}}\) mean?

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) toproduce a true statement. $$\left(4 \times 10^{3}\right)+\left(3 \times 10^{2}\right)=4.3 \times 10^{3}$$

Exercises \(142-144\) will help you prepare for the material covered in the next section. Multiply: \(\quad\left(2 x^{3} y^{2}\right)\left(5 x^{4} y^{7}\right)\)
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