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SSAT Upper Level Math : Properties of Exponents

Study concepts, example questions & explanations for SSAT Upper Level Math

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Example Questions

Example Question #21 : Properties Of Exponents

Which of the values below is equal to $4^{3}$ ?

Possible Answers:

Correct answer:

Explanation:

$4^{3}$ is equal to $4\cdot4\cdot4$

$4\cdot4=16$

Therefore, $4\cdot4\cdot4=16\cdot4=64$

Thus, 64 is the correct answer.

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Example Question #22 : Properties Of Exponents

Which of the values below is equal to $2^{5}$ ?

Possible Answers:

Correct answer:

Explanation:

$2^{5}$ is equal to $2\cdot2\cdot2\cdot2\cdot2$

Given that $2\cdot2=4$ , the above expression can be simplified to:

$4\cdot4\cdot2=16\cdot2=32$

Therefore, 32 is the correct answer.

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Example Question #23 : Properties Of Exponents

Which of the following is equal to 27?

Possible Answers:

$5^{2}$

$3\cdot2^{2}$

$3^{4}$

$3^{3}$

Correct answer:

$3^{3}$

Explanation:

$3^{3}$ is equal to $3\cdot3\cdot3$ .

Given that $3\cdot3=9$ , it follows that

$3\cdot3\cdot3=9\cdot3=27$ .

Therefore, $3^{3}$ is the correct answer.

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Example Question #24 : Properties Of Exponents

Evaluate:

$3^{-2}\times3^{-6}\times3^{6}$

Possible Answers:

$\frac{1}{9}$

$\frac{1}{3}$

Correct answer:

$\frac{1}{9}$

Explanation:

The bases of all three terms are alike. Since the terms are of a specific power, the rule of exponents state that the powers can be added if the terms are multiplied.

$3^{-2}\times3^{-6}\times3^{6}= 3^{-2-6+6}= 3^{-2}$

When we have a negative exponent, we we put the number and the exponent as the denominator, over

$\frac{1}{3^2}=\frac{1}{9}$

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Example Question #25 : Properties Of Exponents

Simplify:

$\frac{8x ^{-2}}{(3x)^{2}}$

Possible Answers:

$\frac{8}{9x}$

$\frac{8}{3x ^{4}}$

$\frac{8}{9}$

$\frac{8}{9x ^{4}}$

$\frac{8}{3}$

Correct answer:

$\frac{8}{9x ^{4}}$

Explanation:

$\frac{8x ^{-2}}{(3x)^{2}}$

To solve this problem, we start with the parentheses and exponents in the denominator.

$= \frac{8x ^{-2}}{3^{2}x^{2}} = \frac{8x ^{-2}}{9x^{2}}$

Next, we can bring the x^2 from the denominator up to the numerator by making the exponent negative.

$= \frac{8x ^{-2-2}}{9} = \frac{8x ^{-4}}{9}$

Finally, to get rid of the negative exponent we can bring it back down to the denominator.

$= \frac{8}{9x ^{4}}$

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Example Question #81 : Ssat Upper Level Quantitative (Math)

What is 9^3 written as a multiplication problem?

Possible Answers:

$9\times9\times9\times3$

$9\times9\times9$

$3\times3\times3$

Correct answer:

$9\times9\times9$

Explanation:

When expanding an exponent, we multiply the base by itself for the number indicated by the exponential value.

In this case, our base number is and our exponential value is . So we multiply by itself times.

Remember, the question asks us for the multiplication problem, not the answer to 9^3 . Because of this, $9\times9\times9$ is our correct answer.

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Example Question #21 : Properties Of Exponents

What is 2^7 written as a multiplication problem?

Possible Answers:

128

$7\times2$

$7\times7$

$2\times2\times2\times2\times2\times2\times2$

Correct answer:

$2\times2\times2\times2\times2\times2\times2$

Explanation:

When expanding an exponent, we multiply the base by itself for the number indicated by the exponential value.

In this case, our base number is and our exponential value is . So we multiply by itself times.

Remember, the question asks us for the multiplication problem, not the answer to 2^7 . Because of this, $2\times2\times2\times2\times2\times2\times2$ is our correct answer.

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Example Question #26 : Properties Of Exponents

What is 3^2 written as a multiplication problem?

Possible Answers:

$3\times2$

$3\times3$

Correct answer:

$3\times3$

Explanation:

When expanding an exponent, we multiply the base by itself for the number indicated by the exponential value.

In this case, our base number is and our exponential value is . So we multiply by itself times.

Remember, the question asks us for the multiplication problem, not the answer to 3^2 . Because of this, $3\times3$ is our correct answer.

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Example Question #27 : Properties Of Exponents

What is 4^6 written as a multiplication problem?

Possible Answers:

$6\times6\times6\times6\times6\times6$

$6\times6\times6\times6$

$4\times4\times4\times4\times4\times4$

$4\textup,096$

Correct answer:

$4\times4\times4\times4\times4\times4$

Explanation:

When expanding an exponent, we multiply the base by itself for the number indicated by the exponential value.

In this case, our base number is and our exponential value is . So we multiply by itself times.

Remember, the question asks us for the multiplication problem, not the answer to 4^6 . Because of this, $4\times4\times4\times4\times4\times4$ is our correct answer.

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Example Question #22 : Properties Of Exponents

What is 5^3 written as a multiplication problem?

Possible Answers:

$3\times5$

$5\times5\times5$

125

$5\times3$

Correct answer:

$5\times5\times5$

Explanation:

When expanding an exponent, we multiply the base by itself for the number indicated by the exponential value.

In this case, our base number is and our exponential value is . So we multiply by itself times.

Remember, the question asks us for the multiplication problem, not the answer to 5^3 . Because of this, $5\times5\times5$ is our correct answer.

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All SSAT Upper Level Math Resources

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SSAT Upper Level Math : Properties of Exponents

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #21 : Properties Of Exponents

Example Question #22 : Properties Of Exponents

Example Question #23 : Properties Of Exponents

Example Question #24 : Properties Of Exponents

Example Question #25 : Properties Of Exponents

Example Question #81 : Ssat Upper Level Quantitative (Math)

Example Question #21 : Properties Of Exponents

Example Question #26 : Properties Of Exponents

Example Question #27 : Properties Of Exponents

Example Question #22 : Properties Of Exponents

All SSAT Upper Level Math Resources

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