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Common Core: High School - Number and Quantity : Rational Exponents: CCSS.Math.Content.HSN-RN.A.1

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Example Questions

Example Question #1 : Rational Exponents: Ccss.Math.Content.Hsn Rn.A.1

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

Possible Answers:

$\displaystyle 16$

$\displaystyle 32$

$\displaystyle 4$

$\displaystyle 64$

Correct answer:

$\displaystyle 16$

Explanation:

To evaluate this, let's rewrite the problem.

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

Now lets break down the cube root.

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

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Example Question #2 : Rational Exponents: Ccss.Math.Content.Hsn Rn.A.1

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

Possible Answers:

$\displaystyle 18$

$\displaystyle 72$

$\displaystyle 6$

$\displaystyle 12$

Correct answer:

$\displaystyle 6$

Explanation:

To evaluate this, let's rewrite the problem.

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

Now lets break down the square root.

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

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Example Question #3 : High School: Number And Quantity

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

Possible Answers:

$\displaystyle 6$

4.5 $\displaystyle 4.5$

$\displaystyle 18$

$\displaystyle 3$

Correct answer:

$\displaystyle 3$

Explanation:

To evaluate this, let's rewrite the problem.

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

Now lets break down the square root.

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

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Example Question #4 : High School: Number And Quantity

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

Possible Answers:

$\displaystyle 49$

$\displaystyle 1$

$\displaystyle 28$

$\displaystyle 7$

Correct answer:

$\displaystyle 49$

Explanation:

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

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

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Example Question #5 : High School: Number And Quantity

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

Possible Answers:

$\displaystyle 3$

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

$\displaystyle 1$

1.3333 $\displaystyle 1.3333$

Correct answer:

$\displaystyle 1$

Explanation:

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

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Example Question #6 : High School: Number And Quantity

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

Possible Answers:

$\displaystyle 4$

$\frac{64}{3}$ $\displaystyle \frac{64}{3}$

$\displaystyle 16$

$\frac{16}{3}$ $\displaystyle \frac{16}{3}$

$\displaystyle 3$

Correct answer:

$\displaystyle 4$

Explanation:

To evaluate this, let's rewrite the problem.

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

Now lets break down the cube root.

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

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Example Question #7 : High School: Number And Quantity

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

Possible Answers:

$\displaystyle 10$

1000 $\displaystyle 1000$

$\displaystyle 1$

100 $\displaystyle 100$

Correct answer:

100 $\displaystyle 100$

Explanation:

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

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

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Example Question #8 : High School: Number And Quantity

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

Possible Answers:

$\displaystyle 1$

$\text{Not defined}$ $\displaystyle \text{Not defined}$

$\displaystyle 0$

$\frac{1}{3}$ $\displaystyle \frac{1}{3}$

Correct answer:

$\displaystyle 0$

Explanation:

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

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Example Question #9 : High School: Number And Quantity

Evaluate: $0^{0}$ $\displaystyle 0^{0}$

Possible Answers:

$\displaystyle 0$

$\displaystyle 1$

$\text{Undefined}$ $\displaystyle \text{Undefined}$

$\text{Not possible}$ $\displaystyle \text{Not possible}$

Correct answer:

$\displaystyle 1$

Explanation:

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

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Example Question #10 : High School: Number And Quantity

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

Possible Answers:

20736 $\displaystyle 20736$

144 $\displaystyle 144$

288 $\displaystyle 288$

$\displaystyle 72$

Correct answer:

20736 $\displaystyle 20736$

Explanation:

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

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

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Common Core: High School - Number and Quantity : Rational Exponents: CCSS.Math.Content.HSN-RN.A.1

Study concepts, example questions & explanations for Common Core: High School - Number and Quantity

All Common Core: High School - Number and Quantity Resources

Example Questions

Example Question #1 : Rational Exponents: Ccss.Math.Content.Hsn Rn.A.1

Example Question #2 : Rational Exponents: Ccss.Math.Content.Hsn Rn.A.1

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All Common Core: High School - Number and Quantity Resources

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