Algebra II : Radicals as Exponents

Study concepts, example questions & explanations for Algebra II

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Example Questions

Example Question #1321 : Mathematical Relationships And Basic Graphs

Solve:  \(\displaystyle 27^\frac{1}{3}-16^{\frac{1}{2}}\)

Possible Answers:

\(\displaystyle -\frac{1}{4}\)

\(\displaystyle 1\)

\(\displaystyle -\frac{1}{3}\)

\(\displaystyle -1\)

\(\displaystyle -3\)

Correct answer:

\(\displaystyle -1\)

Explanation:

The denominator of the fractional exponent represents the index of the radical.

Rewrite the expression in radical form.  A radical with an index of 2 is simply the square root of a number.

\(\displaystyle 27^\frac{1}{3}-16^{\frac{1}{2}} = \sqrt[3]{27}-\sqrt{16} = 3-4 = -1\)

The answer is:  \(\displaystyle -1\)

Example Question #41 : Radicals As Exponents

What is \(\displaystyle 125^\frac{7}{3}\) equivalent to?

Possible Answers:

\(\displaystyle (\frac{5}{3})^7\)

\(\displaystyle 5^7\)

\(\displaystyle (\frac{3}{5})^7\)

\(\displaystyle (\frac{1}{5})^7\)

\(\displaystyle \textup{The answer is not given.}\)

Correct answer:

\(\displaystyle 5^7\)

Explanation:

The denominator represents the index of the square root.  The numerator is the  power that the quantity is raised to.

Rewrite the expression as a radical.

\(\displaystyle 125^\frac{7}{3} =( \sqrt[3]{125})^7 = 5^7\)

The answer is:  \(\displaystyle 5^7\)

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