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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #1565 : Gre Quantitative Reasoning

Compare $5^{27}(850)$ and $5^{29}(34)$ .

Possible Answers:

$\small 5^{27}(850) > 5^{29}(34)$

The answer cannot be determined from the information given.

$\small \small 5^{27}(850) < 5^{29}(34)$

$\small \small \small 5^{27}(850) = 5^{29}(34)$

Correct answer:

$\small \small \small 5^{27}(850) = 5^{29}(34)$

Explanation:

To compare these expressions more easily, we'll change the first expression to have $5^{29}$ in front. We'll do this by factoring out 25 (that is, $\small 5^{2}$ ) from 850, then using the fact that $\small 5^{27}*5^{2}=5^{29}$ .

$5^{27}(850)=5^{27}(25*34)=5^{27}(5^2*34)$

When we combine like terms, we can see that $5^{27}(5^2*34)=5^{29}(34)$ . The two terms are therefore both equal to the same value.

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Example Question #1566 : Gre Quantitative Reasoning

Which of the following is equal to $(5^4*5^5)^{20}$ ?

Possible Answers:

$5^{29}$

$25^{180}$

$5^{180}$

$5^{40}$

$25^{29}$

Correct answer:

$5^{180}$

Explanation:

$x^{a} \times x^{b}$ is always equal to $x^{a + b}$ ; therefore, 5 raised to 4 times 5 raised to 5 must equal 5 raised to 9.

$(5^4*5^5)^{20}=(5^{(4+5)})^{20}=(5^9)^{20}$

$(x^{a})^{b}$ is always equal to $x^{(a*b)}$ . Therefore, 5 raised to 9, raised to 20 must equal 5 raised to 180.

$(5^9)^{20}=5^{(9*20)}=5^{180}$

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Example Question #21 : Exponential Operations

Which of the following is equal to ((6^7)(5^7))^7 ?

Possible Answers:

$30^{49}$

$30^{14}$

$12^{49}$

$210^{7}$

$77^{7}$

Correct answer:

$30^{49}$

Explanation:

First, multiply inside the parentheses: (6^7)(5^7)=30^7 .

Then raise to the 7th power: $(30^7)^7=30^{49}$ .

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Example Question #22 : Exponential Operations

Simplify:

$(6x^{2})^{3}\cdot x^{-7}\cdot 2x^{4}$

Possible Answers:

$432x^{3}$

$12x^{2}$

$6x^{2}$

Correct answer:

$432x^{3}$

Explanation:

Remember, we add exponents when their bases are multiplied, and multiply exponents when one is raised to the power of another. Negative exponents flip to the denominator (presuming they originally appear in the numerator).

$(6x^{2})^{3}\cdot x^{-7}\cdot 2x^{4}$

$=\frac{216x^{6}\cdot 2x^{4}}{x^{7}}$

$=\frac{432x^{10}}{x^{7}}$

$=432x^{3}$

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Example Question #2211 : Sat Mathematics

Evaluate:

$y=\frac{3^{13}-9^{5}}{\left ( \frac{1}{27} \right )^{-3}}$

Possible Answers:

$\dpi{100} \small 78$

$\dpi{100} \small 27$

$\dpi{100} \small 81$

$\dpi{100} \small 30$

$\dpi{100} \small 24$

Correct answer:

$\dpi{100} \small 78$

Explanation:

Can be simplified to:

Capture2

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Example Question #2212 : Sat Mathematics

2^3*2^4

Possible Answers:

$2^{12}$

2^7

2^4-3

2^1

2^3*3

Correct answer:

2^7

Explanation:

When multplying exponents, we need to make sure we have the same base.

Since we do, all we have to do is add the exponents.

The answer is $2^{3+4}=2^7$ .

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Example Question #31 : Exponents

$3^4*3^{15}*3^2$

Possible Answers:

3^9

3^5-9

$3^{15}-2$

$3^{21}$

$3^{20}+2$

Correct answer:

$3^{21}$

Explanation:

When multplying exponents, we need to make sure we have the same base.

Since we do, all we have to do is add the exponents.

The answer is $3^{4+15+2}=3^{21}$ .

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Example Question #32 : Exponents

6^7*6^8*6^9

Possible Answers:

$6^{24}$

$6^{65}$

$6^{-8}$

$6^{-1}$

$6^{504}$

Correct answer:

$6^{24}$

Explanation:

When multplying exponents, we need to make sure we have the same base.

Since we do, all we have to do is add the exponents.

The answer is $6^{7+8+9}=6^{24}$ .

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Example Question #33 : Exponents

9^5*9^4*9^0

Possible Answers:

9^8

9^1

$9^{20}$

9^9

Correct answer:

9^9

Explanation:

When multplying exponents, we need to make sure we have the same base.

Since we do, all we have to do is add the exponents.

The answer is $9^{5+4+0}=9^9$ .

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Example Question #34 : Exponents

$7^{-6}*{7^5}$

Possible Answers:

$7^{-30}$

$7^{11}$

$7^{-1}$

$7^{-11}$

Correct answer:

$7^{-1}$

Explanation:

When multplying exponents, we need to make sure we have the same base.

Since we do, all we have to do is add the exponents.

Since there is a negative sign, we compare. is greater than and is negative so our answer must be negative. We treat the equation as a subtraction problem.

The answer is $7^{-6+5}=7^{-1}$ .

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1565 : Gre Quantitative Reasoning

Example Question #1566 : Gre Quantitative Reasoning

Example Question #21 : Exponential Operations

Example Question #22 : Exponential Operations

Example Question #2211 : Sat Mathematics

Example Question #2212 : Sat Mathematics

Example Question #31 : Exponents

Example Question #32 : Exponents

Example Question #33 : Exponents

Example Question #34 : Exponents

All SAT Math Resources

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