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}

Example: evaluate 27^{\frac23}

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

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

Example: evaluate 81^{\frac12}

flashcards

QuestionAnswer
When raising a number to a fraction, what does the denominator of the fraction represent?The denominator is the order of the root.
What is the general rule for a^{\frac{x}{y}}?a^{\frac{x}{y}} = (\sqrt[y]{a})^x
Evaluate 16^{\frac{3}{4}}(\sqrt[4]{16})^3 = 2^3 = 8
Evaluate 27^{\frac{2}{3}}(\sqrt[3]{27})^2 = 3^2 = 9
Write x^{\frac{1}{3}} in surd form\sqrt[3]{x}
Write a^{\frac{2}{5}} in surd form(\sqrt[5]{a})^2
Evaluate 81^{\frac{1}{2}}\sqrt{81} = 9