GMAT Math : Exponents

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Example Question #81 : Understanding Exponents

is the additive inverse of the multiplicative inverse of ; is the additive inverse of the multiplicative inverse of . Which of the following is equal to the expression

$(AB)^{CD}$

regardless of the values of the variables?

Possible Answers:

$(AB)^{CD}$ is an undefined quantity

Correct answer:

Explanation:

The additive inverse of a number is the number which, when added to that number, yields sum 0; the multiplicative inverse of a number is the number which, when multiplied by that number, yields product 1.

Let be the multiplicative inverse of . Then

BX= 1 , or, equivalently, $X = \frac{1}{B}$ .

is the additive inverse of this number, so

A + X = 0

$A + \frac{1}{B}= 0$

$A = - \frac{1}{B}$

$A \cdot B = - \frac{1}{B} \cdot B$

AB = -1

By similar reasoning, CD = -1 , and

$(AB)^{CD} = \left ( -1\right ) ^{-1} = \frac{1}{-1} = -1$

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Example Question #82 : Understanding Exponents

$FG= 2^{100}$

$HJ = 2^{10}$

$\frac{F}{J} = 4^{40}$

Which of the following is equal to $\frac{H}{G}$ ?

Possible Answers:

$\frac{1}{2^{130}}$

$\frac{1}{2^{170}}$

$\frac{1}{2^{10}}$

$\frac{1}{2^{50}}$

$\frac{1}{2^{70}}$

Correct answer:

$\frac{1}{2^{10}}$

Explanation:

Divide:

$\frac{HJ}{FG}=\frac{ 2^{10}}{2^{100}} = 2^{10-100} = 2^{-90}$

$\frac{HJ}{FG}= \frac{H}{G} \cdot \frac{J}{F} = \frac{H}{G} \div \frac{F} {J}$

$\frac{F}{J} = 4^{40} = (2 ^{2})^{40} = 2 ^{2 \cdot 40 } = 2 ^{80}$

Substitute:

$\frac{H}{G} \div \frac{F} {J} = \frac{HJ}{FG}$

$\frac{H}{G} \div 2 ^{80}= 2^{-90}$

$\frac{H}{G} \div 2 ^{80}\cdot 2 ^{80} = 2^{-90} \cdot 2 ^{80}$

$\frac{H}{G} = 2^{-90+ 80} = 2^{-10} = \frac{1}{2^{10}}$

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Example Question #83 : Understanding Exponents

is the additive inverse of ; is the multiplicative inverse of . Which of the following is equal to the expression

$(A+B)^{C+D}$

regardless of the values of the variables?

Possible Answers:

$(A+B)^{C+D}$ must be an undefined quantity.

$A + \frac{1}{A}$

$A - \frac{1}{A}$

Correct answer:

Explanation:

The additive inverse of a number is the number which, when added to that number, yields sum 0. Since is the additive inverse of ,

A + B = 0

The multiplicative inverse of a number is the number which, when multiplied by that number, yields product 1. Since is the multiplicative inverse of , then

CD = 1 , or $D = \frac{1}{C}$ .

It follows that

$(A+B)^{C+D} = 0^{C+ \frac{1}{C}}$ .

0 raised to any nonzero power is equal to 0, and $C + \frac{1}{C}$ must be nonzero, so

$0^{C+ \frac{1}{C}} = 0$ , the correct response.

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Example Question #84 : Understanding Exponents

is the additive inverse of ; is the additive inverse of . Which of the following is equal to the expression

$(A+B)^{C+D}$

regardless of the values of the variables?

Possible Answers:

$(A+B)^{C+D}$ must be an undefined quantity

$A - \frac{1}{A}$

$A + \frac{1}{A}$

Correct answer:

$(A+B)^{C+D}$ must be an undefined quantity

Explanation:

The additive inverse of a number is the number which, when added to that number, yields sum 0. Since is the additive inverse of and is the additive inverse of ,

A + B = C+D = 0

and

$(A+B)^{C+D} = 0^{0}$ ,

which is an undefined expression.

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GMAT Math : Exponents

Study concepts, example questions & explanations for GMAT Math

All GMAT Math Resources

Example Questions

Example Question #81 : Understanding Exponents

Example Question #82 : Understanding Exponents

Example Question #83 : Understanding Exponents

Example Question #84 : Understanding Exponents

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