GMAT Math : Understanding powers and roots

Study concepts, example questions & explanations for GMAT Math

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Example Questions

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Example Question #1 : Understanding Powers And Roots

Solve: \frac{(0.5)^{6}}{(0.5)^{9}}

Possible Answers:

\dpi{100} \small 125

\dpi{100} \small 0.125

\dpi{100} \small 8

\dpi{100} \small 0.25

\dpi{100} \small 4

Correct answer:

\dpi{100} \small 8

Explanation:

Solve\dpi{100} \small : \frac{0.5^{6}}{0.5^{9}} = 0.5^{6-9}= 0.5^{-3}=\frac{1}{0.5^{3}}=\frac{1}{0.125} = 8

Example Question #2 : Understanding Powers And Roots

\frac{x^{2}y^{3}z^{4}}{x^{3}yz^{3}} =

Possible Answers:

\frac{y^{2}z}{x}

\dpi{100} \small cannot\ be\ simplified

\frac{yz}{x}

\frac{1}{x^{2}}

\frac{yz}{x^{2}}

Correct answer:

\frac{y^{2}z}{x}

Explanation:

\frac{x^{2}y^{3}z^{4}}{x^{3}yz^{3}} = \frac{y^{3-1}z^{4-3}}{x^{3-2}} = \frac{y^{2}z}{x}

Example Question #3 : Understanding Powers And Roots

Solve: \small (\sqrt{5}+\sqrt{4})^2

Possible Answers:

\small 20

\small 20+4\sqrt5

\small 9+4\sqrt5

\small 9

Correct answer:

\small 9+4\sqrt5

Explanation:

First, FOIL:

\small (\sqrt5+\sqrt4)^2=(\sqrt5+\sqrt4)(\sqrt5+\sqrt4)=5+\sqrt20+\sqrt20+4

\small =9+2\sqrt20

Factor out \small \sqrt4

\small =9+4\sqrt5

Example Question #32 : Arithmetic

Solve: \small \frac{10^9-10^7}{99}

Possible Answers:

\small \frac{10}{99}

\small 10^7

\small \frac{100}{99}

\small \frac{10^7}{99}

Correct answer:

\small 10^7

Explanation:

First factor. \small \frac{10^9-10^7}{99}\ =\ \frac{(10^7)(10^2-1)}{99}

Simplify. \small \frac{(10^7)(10^2-1)}{99}\ =\ \frac{(10^7)(100-1)}{99}\ =\ \frac{(10^7)(99)}{99}\ =\ 10^7

Example Question #33 : Arithmetic

If \small x^2=8, what is \small x^4?

Possible Answers:

Correct answer:

Explanation:

\small x^4=(x^2)^2=(8)^2=64

Example Question #34 : Arithmetic

Evaluate: 

Possible Answers:

Correct answer:

Explanation:

Example Question #35 : Arithmetic

Simplify this expression as much as possible:

Possible Answers:

The expression cannot be simplified further


Correct answer:

Explanation:

Example Question #36 : Arithmetic

If the side length of a cube is tripled, how does the volume of the cube change?

Possible Answers:

Volume becomes 3 times larger.

Volume becomes 27 times larger.

Volume becomes 9 times larger.

The volume doesn't change.

Not enough informatin is given.

Correct answer:

Volume becomes 27 times larger.

Explanation:

The equation for the volume of a cube is .  If the length is tripled, it becomes , and , so the volume increases by 27 times the original size.

Example Question #37 : Arithmetic

Simplify 

Possible Answers:

Correct answer:

Explanation:

This can either be done by brute force (slow) or by recognizing the properties of roots and exponents (fast).  Roots are simply fractional exponents: , , etc. so they can be done in any order.

 

So we see a cube root, we can immediately cancel that with the exponent of 3. taking us from here: to .  We now simplify to get

Example Question #38 : Arithmetic

In the sequence 1, 3, 9, 27, 81, … , each term after the first is three times the previous term. What is the sum of the 9th and 10th terms in the sequence?

Possible Answers:

Correct answer:

Explanation:

We can rewrite the sequence as , , , , , … ,

and we can see that the 9th term in the sequence is and the 10th term in the sequence is . Therefore, the sum of the 9th and 10th terms would be


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