The Real Number System - Common Core: High School - Number and Quantity

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Question

Evaluate: $100^{\frac{1}{2}}$

Answer

To evaluate this, let's rewrite the problem.

$100^{\frac{1}{2}}=\sqrt{100}$

Now lets break down the square root.

$\sqrt{100}=\sqrt{10\cdot10}=\sqrt{10^2}=10$

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Question

Evaluate: $64^{\frac{1}{3}}$

Answer

To evaluate this, let's rewrite the problem.

$64^{\frac{1}{3}}=\sqrt[3]{64}$

Now lets break down the cube root.

$\sqrt[3]{64}=\sqrt[3]{4\cdot4\cdot4}=\sqrt[3]{4^3}=4$

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Question

Evaluate: $64^{\frac{2}{3}}$

Answer

To evaluate this, let's rewrite the problem.

$64^{\frac{2}{3}}=(\sqrt[3]{64})^2$

Now lets break down the cube root.

$(\sqrt[3]{64})^2=(\sqrt[3]{4\cdot4\cdot4})^2=(\sqrt[3]{4^3})^2=4^2=16$

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Question

Evaluate: $36^{\frac{1}{2}}$

Answer

To evaluate this, let's rewrite the problem.

$36^{\frac{1}{2}}=\sqrt{36}$

Now lets break down the square root.

$\sqrt{36}=\sqrt{6\cdot6}=\sqrt{6^2}=6$

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Question

Evaluate: $9^{\frac{1}{2}}$

Answer

To evaluate this, let's rewrite the problem.

$9^{\frac{1}{2}}=\sqrt{9}$

Now lets break down the square root.

$\sqrt{9}=\sqrt{3\cdot3}=\sqrt{3^2}=3$

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Question

Evaluate: $49^{\frac{2}{2}}$

Answer

To solve this, let's reduce the exponent, and then solve.

$49^{\frac{2}{2}}=49^{\frac{1}{1}}=49^1=49$

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Question

Evaluate: $1^{\frac{1}{3}}$

Answer

One to any power is just , so $1^{\frac{1}{3}}=1$

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Question

Evaluate: $144^{\frac{4}{2}}$

Answer

The first part to solving this problem is reducing the exponent, and then solving.

$144^{\frac{4}{2}}=144^{\frac{2}{1}}=144^2=20736$

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Question

Evaluate: $100^{\frac{2}{2}}$

Answer

To solve this, let's reduce the exponent, and then solve.

$100^{\frac{2}{2}}=100^{\frac{1}{1}}=100^1=100$

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Question

Evaluate: $0^{\frac{1}{3}}$

Answer

Zero to any power is just , expect when the power is . So $0^{\frac{1}{3}}=0$

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Question

Evaluate: $0^{0}$

Answer

Zero raised to the zero is equal to one, otherwise it is equal to zero. $0^{0}=1$

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Question

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

Answer

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.

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

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Question

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

Answer

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.

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

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Question

Rewrite $92^{\frac{3}{4}}$ , in radical form.

Answer

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 .

$92^{\frac{3}{4}}=(\sqrt[4]{92})^3$

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Question

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

Answer

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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Question

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

Answer

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 .

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

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Question

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

Answer

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.

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

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Question

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

Answer

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.

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

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Question

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

Answer

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 .

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

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Question

Rewrite $58^{\frac{2}{7}}$ , in radical form.

Answer

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 .

$58^{\frac{2}{7}}=(\sqrt[7]{58})^2$

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