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Chapter 0: Problem 95

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

Short Answer

Expert verified
The simplified form of the given expression \(\left(x^{\frac{2}{3}}\right)^{3}\) is \(x^{2}\).

Step by step solution

01

Apply the Power of a Power Rule to the expression

In the given expression, \(\left(x^{\frac{2}{3}}\right)^{3}\), the Power of a Power Rule is applied to multiply the exponents. When we multiply the exponents \(\frac{2}{3}\) and 3, the output is 2 as \(\frac{2}{3}\) * 3 equals 2.
02

Simplify to obtain the final expression

After applying the multiplication of exponents, the expression simplifies down to \(x^{2}\). This is the simplified exponent expression.

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Most popular questions from this chapter

Why is \(\left(-3 x^{2}\right)\left(2 x^{-5}\right)\) not simplified? What must be done to simplify the expression?

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

Factor completely. $$ (x-5)^{-\frac{1}{2}}(x+5)^{-\frac{1}{2}}-(x+5)^{\frac{1}{2}}(x-5)^{-\frac{3}{2}} $$

Simplify using properties of exponents. $$\frac{\left(2 y^{\frac{1}{5}}\right)^{4}}{y^{\frac{3}{10}}}$$

Find the exact value of \(\sqrt{13+\sqrt{2}+\frac{7}{3+\sqrt{2}}}\) without the use of a calculator.
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