Rational Exponents and Radicals

a

We begin by rewriting the rational exponents as radicals. Then we can simplify one term at a time.

3 + 9^{\frac{1}{2}} - 3^{\frac{1}{2}} \cdot 3^{\frac{1}{2}}

a^{\frac{1}{2}} = a

3 + 9 - 3 \cdot 3

CalcRootCalculate root

3 + 3 - 3 \cdot 3

MultSqrt

a \cdot a = a

3 + 3 - 3

AddSubTermsAdd and subtract terms

3

b

We will simplify the expression one term at a time. We can use the properties of exponents to simplify the term $4^{\frac{1}{3}} \cdot 4^{\frac{2}{3}} .$

2 - 8^{\frac{1}{3}} + 4^{\frac{1}{3}} \cdot 4^{\frac{2}{3}}

PowToRootD

a^{\frac{1}{n}} = n a

2 - 38 + 4^{\frac{1}{3}} \cdot 4^{\frac{2}{3}}

CalcRootCalculate root

2 - 2 + 4^{\frac{1}{3}} \cdot 4^{\frac{2}{3}}

MultPow

a^{m} \cdot a^{n} = a^{m + n}

2 - 2 + 4^{\frac{1}{3} + \frac{2}{3}}

AddFracAdd fractions

2 - 2 + 4^{\frac{3}{3}}

QuotOne

\frac{a}{a} = 1

2 - 2 + 4^{1}

ExponentOne

a^{1} = a

2 - 2 + 4

AddSubTermsAdd and subtract terms

4

Rational Exponents and Radicals 1.15 - Solution