GMAT Math : Powers & Roots of Numbers

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Example Question #11 : Understanding Powers And Roots

What is 4^3 ?

Possible Answers:

128

Correct answer:

Explanation:

4^3=4*4*4=16*4=64

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Example Question #12 : Understanding Powers And Roots

What is 2^5 ?

Possible Answers:

Correct answer:

Explanation:

2^5=2*2*2*2*2=4*4*2=16*2=32

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Example Question #11 : Powers & Roots Of Numbers

What is $\sqrt{81}$ ?

Possible Answers:

Correct answer:

Explanation:

9*9=81

$\sqrt{81}=9$

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Example Question #12 : Powers & Roots Of Numbers

What is $\sqrt{225}$ ?

Possible Answers:

112

Correct answer:

Explanation:

15*15=225

$\sqrt{225}=15$

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Example Question #13 : Powers & Roots Of Numbers

What is $\sqrt[3]{64}$ ?

Possible Answers:

Correct answer:

Explanation:

4*4*4=64

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

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Example Question #14 : Powers & Roots Of Numbers

Which of the following is equivalent to $\left (81 x \right )^{\frac{3}{4}}$ ?

Possible Answers:

$27x \sqrt[3]{ x }$

$27x \sqrt[3]{3 x }$

$3x \sqrt[3]{3 x }$

$27 \sqrt[4]{ x^{3} }$

$3 \sqrt[4]{27x^{3} }$

Correct answer:

$27 \sqrt[4]{ x^{3} }$

Explanation:

$\left (81 x \right )^{\frac{3}{4}} =\left ( \sqrt[4]{ 81 x } \right) ^{3} = \left ( \sqrt[4]{ 81 } \right) ^{3} \cdot\left ( \sqrt[4]{ x } \right) ^{3}= 3^{3} \sqrt[4]{ x^{3} } = 27 \sqrt[4]{ x^{3} }$

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Example Question #15 : Powers & Roots Of Numbers

$3^{5}\cdot 3^{2}=$

Possible Answers:

$9^{3}$

$3^{7}$

$3^{10}$

$9^{7}$

Correct answer:

$3^{7}$

Explanation:

The two terms have the same base, 3. Therefore, we add the exponents to simplify:

$3^{5}\cdot 3^{2}=3^{5+2}=3^7$

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Example Question #18 : Powers & Roots Of Numbers

Find the remainder

$\frac{75^{75}}{38}$

Possible Answers:

Correct answer:

Explanation:

Clearly, we aren't expected to calculate 75^75. The clue is that since we are supposed to divide by 38, let's see if we can rewrite the numerator so that we have a 38 in it.

For example: $75^{75}=(76-1)^{75}$ ,

and 76=2*38 ,

so we have:

$75^{75}=(2*38-1)^{75}$

If we expanded this expression, all of the terms but one will have a in them, so all of the terms except for the last term, when divided by , will not leave a remainder.

The last term will be $(-1)^{75}$ , which is just .

Essentially, all we are asked to do is to figure out the remainder when is divided by .

Otherwise stated:

-1=38(-1)+R , where R is the remainder.

Clearly, R=37

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Example Question #19 : Powers & Roots Of Numbers

Kite

Give the area of the above kite.

Possible Answers:

168

175

The area cannot be determined from the information given.

Correct answer:

168

Explanation:

$7^{2}+ 24^{2}= 49 + 576 = 625 = 25^{2}$ ,

so the lengths of the sides of each triangle comprise a Pythagorean triple. Therefore, each triangle is a right triangle with legs 7 and 24, and the kite is a composite of two such right triangles. Its area is therefore

$2 \times \frac{1}{2} \times 7 \times 24 = 168$

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Example Question #20 : Powers & Roots Of Numbers

Which of the following expressions is equivalent to $x^{\frac{2}{3}}$ ?

You may assume that is positive.

Possible Answers:

$\sqrt[3]{x^{2}}$

$\sqrt[3]{2x}$

None of the other responses is correct.

$x\sqrt{x}$

$\sqrt{3x}$

Correct answer:

$\sqrt[3]{x^{2}}$

Explanation:

For all integers M,N and all positive bases ,

$a^{ \frac{M}{N}} = \sqrt[N]{a^{M}}$ by definition.

Set a = x, M = 2, N = 3 :

$x^{\frac{2}{3}}= \sqrt[3]{x^{2}}$

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GMAT Math : Powers & Roots of Numbers

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #11 : Understanding Powers And Roots

Example Question #12 : Understanding Powers And Roots

Example Question #11 : Powers & Roots Of Numbers

Example Question #12 : Powers & Roots Of Numbers

Example Question #13 : Powers & Roots Of Numbers

Example Question #14 : Powers & Roots Of Numbers

Example Question #15 : Powers & Roots Of Numbers

Example Question #18 : Powers & Roots Of Numbers

Example Question #19 : Powers & Roots Of Numbers

Example Question #20 : Powers & Roots Of Numbers

All GMAT Math Resources

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