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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #135 : Exponential Operations

$\frac{19^{-7}}{19^{-7}}$

Possible Answers:

$19^{14}$

$19^{-14}$

$19^{49}$

Correct answer:

Explanation:

When dividing exponents, we need to make sure we have the same base. In this case we do. Since we are subtracting with a negative value, then it becomes addition. So far, we have -7+7 . This is essentially . Anything except raised to power is . Answer is .

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Example Question #22 : How To Divide Exponents

$\frac{9^4}{27^2}$

Possible Answers:

9^2

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

27^2

3^2

3^8

Correct answer:

3^2

Explanation:

When dividing exponents, we need to make sure we have the same base. In this case we don't. However we can convert 9, 27 to bases of . 9=3^2, 27=3^3 .We have changed the base and need to determine the exponent by doing a proportion. $\frac{1}{2}=\frac{4}{x}$ . The top represents the power raised from base . The bottom represents the power raised from base . When we cross-multiply, we get . 9^4=3^8

$\frac{1}{3}=\frac{2}{x}$ . The top represents the power raised from base . The bottom represents the power raised from base . When we cross-multiply, we get . 27^2=3^6

We now have the same bases and now we just subtract the exponents. The answer is $3^{8-6}=3^2$ .

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Example Question #137 : Exponential Operations

$\frac{9^{12}}{3^5}$

Possible Answers:

3^7

$3^{60}$

$3^{19}$

$3^{29}$

27^7

Correct answer:

$3^{19}$

Explanation:

When dividing exponents, we need to make sure we have the same base. In this case we don't, but 9=3^2 .We have changed the base and need to determine the exponent by doing a proportion. $\frac{1}{2}=\frac{12}{x}$ . The top represents the power raised from base . The bottom represents the power raised from base . When we cross-multiply, we get . We now have the same bases and now we just subtract the exponents. The answer is $3^{24-5}=3^{19}$ .

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Example Question #138 : Exponential Operations

$\frac{4^2}{2^3}$

Possible Answers:

$2^{-1}$

Cannot be determined

8^6

$2^{1.5}$

Correct answer:

Explanation:

When dividing exponents, we need to make sure we have the same base. In this case we don't, but 4=2^2 .We have changed the base and need to determine the exponent by doing a proportion. $\frac{1}{2}=\frac{2}{x}$ . The top represents the power raised from base . The bottom represents the power raised from base . When we cross-multiply, we get . We now have the same bases and now we just subtract the exponents. The answer is $2^{4-3}=2^1=2$ .

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Example Question #139 : Exponential Operations

$\frac{3^5*2^5}{6^7}$

Possible Answers:

Cannot be determined

$6^{35}$

$6^{-2}$

$6^{12}$

6^2

Correct answer:

$6^{-2}$

Explanation:

When dividing exponents, we need to make sure we have the same base. In this case we don't. However, 6=2*3 . To convert to base of , we need to ensure the and base are raised to the same exponent. They are so therefore 2^5*3^5=6^5 . With same base now, we can subtract the exponents. The answer is $6^{5-7}=6^{-2}$ .

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Example Question #2321 : Sat Mathematics

Simplify:

$\frac{\left ( 5 st^{2} \right )^{3}}{s^{4} \cdot 50 t}$

Possible Answers:

$\frac{ 3 t^{4} }{10s }$

$\frac{ 5 t^{5} }{2s }$

None of the other responses gives a correct answer.

$\frac{ 5 t^{4} }{2s }$

$\frac{ 3 t^{5} }{10s }$

Correct answer:

$\frac{ 5 t^{5} }{2s }$

Explanation:

$\frac{\left ( 5 st^{2} \right )^{3}}{s^{4} \cdot 50 t}$

$=\frac{5^{3} s^{3}\left ( t^{2} \right )^{3}}{50 s^{4} t}$

$=\frac{125 s^{3}\cdot t^{2 \cdot 3} }{50 s^{4} t}$

$=\frac{125 s^{3} t^{6} }{50 s^{4} t}$

$=\frac{125 }{50 } \cdot \frac{s^{3} t^{6} }{s^{4} t}$

$=\frac{5 }{2 } \cdot \frac{ t^{6-1} }{s^{4-3} }$

$=\frac{5 }{2 } \cdot \frac{ t^{5} }{s^{1} }$

$= \frac{ 5 t^{5} }{2s }$

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Example Question #2322 : Sat Mathematics

Evaluate $7^{90}\div7^{16}$

Possible Answers:

$7^{35}$

$7^{74}$

$7^{25}$

7^5

$7^{18}$

Correct answer:

$7^{74}$

Explanation:

When dividing exponents with the same base, we just subtract the exponents and keep the base the same.

$7^{90}\div7^{16}=7^{90-16}=7^{74}$

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Example Question #2323 : Sat Mathematics

Evaluate $9^8\div9^{-3}$

Possible Answers:

9^5

$9^{11}$

9^6

$9^{-12}$

$9^{-24}$

Correct answer:

$9^{11}$

Explanation:

When dividing exponents with the same base, we just subtract the exponents and keep the base the same.

$9^8\div9^{-3}=9^{8-(-3)}=9^{11}$

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Example Question #2324 : Sat Mathematics

Evaluate $16^5\div2^{12}$

Possible Answers:

2^8

4^6

2^9

$2^{-7}$

$8^{-7}$

Correct answer:

2^8

Explanation:

Although we have different bases, we know that 16=2^4 . Therefore we know that $(2^4)^5\div2^{12}=2^{20-12}=2^8$

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Example Question #2325 : Sat Mathematics

Solve:

$\frac{x^{6}}{x^{2}}$

Possible Answers:

$x^{8}$

$x^{4}$

$x^{12}$

$x^{3}$

Correct answer:

$x^{4}$

Explanation:

When dividing expressions with the same variable, combine terms by subtracting the exponents, while leaving the variable unchanged. For this problem, we do that by subtracting 6-2, to get a new exponent of 4:

$\frac{x^{6}}{x^{2}}=x ^{6-2}=x^{4}$

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SAT Math : SAT Mathematics

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #135 : Exponential Operations

Example Question #22 : How To Divide Exponents

Example Question #137 : Exponential Operations

Example Question #138 : Exponential Operations

Example Question #139 : Exponential Operations

Example Question #2321 : Sat Mathematics

Example Question #2322 : Sat Mathematics

Example Question #2323 : Sat Mathematics

Example Question #2324 : Sat Mathematics

Example Question #2325 : Sat Mathematics

All SAT Math Resources

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