Fractional powers

When we raise a number to a fraction, the denominator of the fraction is the order of the root.

a^{\frac xy}=(\sqrt[y]{a})^b

Example: evaluate 16^{\frac34}

• =(\sqrt[4]{16})^3
• =2^3
• =8

Example: evaluate 27^{\frac23}

• =(\sqrt[3]{27})^2
• =3^2
• =9

Example: write x^{\frac13} in surd form

• =\sqrt[3]{x}

Example: write a^{\frac25} in surd form

• =(\sqrt[5]{a})^2

Example: evaluate 81^{\frac12}

• =\sqrt{81}
• =9