Rewrite Radical and Rational Exponent Expressions: CCSS.Math.Content.HSN-RN.A.2

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Common Core: High School - Number and Quantity › Rewrite Radical and Rational Exponent Expressions: CCSS.Math.Content.HSN-RN.A.2

Questions 1 - 10

Rewrite $31^{\frac{5}{6}}$ , in radical form.

$(\sqrt[6]{31})^5$

$(\sqrt[5]{31})^6$

$\sqrt[6]{\frac{31}{5}}$

$\sqrt[5]{\frac{31}{6}}$

Explanation

To determine what the root is, we look at the denominator of the exponent. In this case the root is , and the numerator tells us what power we are raising the entire expression to, which is .

$31^{\frac{5}{6}}=(\sqrt[6]{31})^5$

Rewrite $111^{\frac{5}{6}}$ , in radical form.

$(\sqrt[6]{111})^5$

$(\sqrt[5]{111})^6$

$\sqrt[5]{\frac{111}{6}}$

$\sqrt[6]{\frac{111}{5}}$

Explanation

To determine what the root is, we look at the denominator of the exponent. In this case the root is , and the numerator tells us what power we are raising the entire expression to, which is .

$111^{\frac{5}{6}}=(\sqrt[6]{111})^5$

Rewrite $17^{\frac{1}{5}}$ , in radical form.

$\sqrt[5]{17}$

$17^{\frac{1}{5}}$

$\sqrt[17]{5}$

$\sqrt[5]{\frac{17}{5}}$

Explanation

To determine what the root is, we look at the denominator of the exponent. In this case the root is , so we will write it in the following way.

$17^{\frac{1}{5}}=\sqrt[5]{17}$

Rewrite $79^{\frac{2}{3}}$ , in radical form.

$(\sqrt[3]{79})^2$

$(\sqrt[2]{79})^3$

$\sqrt[3]{\frac{79}{2}}$

$\sqrt[]{\frac{79}{3}}$

Explanation

To determine what the root is, we look at the denominator of the exponent. In this case the root is , and the numerator tells us what power we are raising the entire expression to, which is .

$79^{\frac{2}{3}}=(\sqrt[3]{79})^2$

Rewrite $86^{\frac{1}{6}}$ , in radical form.

$\sqrt[6]{86}$

$86^{\frac{1}{6}}$

$\sqrt[86]{6}$

$\sqrt[6]{\frac{86}{6}}$

Explanation

To determine what the root is, we look at the denominator of the exponent. In this case the root is , so we will write it in the following way.

$86^{\frac{1}{6}}=\sqrt[6]{86}$

Rewrite $56^{\frac{5}{4}}$ , in radical form.

$(\sqrt[4]{56})^5$

$(\sqrt[5]{56})^4$

$\sqrt[5]{\frac{56}{4}}$

$\sqrt[4]{\frac{56}{5}}$

Explanation

To determine what the root is, we look at the denominator of the exponent. In this case the root is , and the numerator tells us what power we are raising the entire expression to, which is .

$56^{\frac{5}{4}}=(\sqrt[4]{56})^5$

Rewrite $116^{\frac{1}{5}}$ , in radical form.

$\sqrt[5]{116}$

$116^{\frac{1}{5}}$

$\sqrt[116]{5}$

$\sqrt[5]{\frac{116}{5}}$

Explanation

To determine what the root is, we look at the denominator of the exponent. In this case the root is , so we will write it in the following way.

$116^{\frac{1}{5}}=\sqrt[5]{116}$

Rewrite $84^{\frac{1}{3}}$ , in radical form.

$\sqrt[3]{84}$

$84^{\frac{1}{3}}$

$\sqrt[3]{\frac{84}{3}}$

$\sqrt[84]{3}$

Explanation

To determine what the root is, we look at the denominator of the exponent. In this case the root is , so we will write it in the following way.

$84^{\frac{1}{3}}=\sqrt[3]{84}$

Rewrite $134^{\frac{1}{2}}$ , in radical form.

$\sqrt{134}$

$134^{\frac{1}{2}}$

$\sqrt[]{\frac{134}{2}}$

$\sqrt[134]{2}$

Explanation

To determine what the root is, we look at the denominator of the exponent. In this case the root is , so we will write it in the following way.

$134^{\frac{1}{2}}=\sqrt[]{134}$

Rewrite $59^{\frac{3}{8}}$ , in radical form.

$(\sqrt[8]{59})^3$

$(\sqrt[3]{59})^8$

$\sqrt[8]{\frac{59}{3}}$

$\sqrt[3]{\frac{59}{8}}$

Explanation

To determine what the root is, we look at the denominator of the exponent. In this case the root is , and the numerator tells us what power we are raising the entire expression to, which is .

$59^{\frac{3}{8}}=(\sqrt[8]{59})^3$

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