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SAT Math : Exponential Operations

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Example Questions

Example Question #131 : Exponents

$\frac{10^{12}}{10^{10}}$

Possible Answers:

1000

$10^{120}$

$10^{1200}$

$10^{22}$

100

Correct answer:

100

Explanation:

When dividing exponents, we need to make sure we have the same base. In this case we do. Then we just subtract the exponents. The answer is $10^{12-10}=10^2$ . 10^2 is just 10*10 or 100 .

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Example Question #131 : Exponential Operations

$\frac{4^7}{4^-8}$

Possible Answers:

$4^{-1}$

$4^{56}$

$4^{-15}$

$4^{-56}$

$4^{15}$

Correct answer:

$4^{15}$

Explanation:

When dividing exponents, we need to make sure we have the same base. In this case we do. Then we just subtract the exponents. Since we arre subtracting wit a negative alue, this becomes an addition problem. The answer is $4^{7-(-8)}=4^{7+8}=4^{15}$ .

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Example Question #133 : Exponential Operations

$\frac{9^{-7}}{9^{-8}}$

Possible Answers:

$9^{-1}$

$9^{-15}$

$9^{15}$

9^2

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+8 . Since is greater than and is positive, the answer must be positive. We just treat this as a subtraction problem. The answer is $9^{-7-(-8)}=9^{-7+8}=9$ .

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Example Question #132 : Exponential Operations

$\frac{13^{-3}}{13^6}$

Possible Answers:

$13^{18}$

$13^{-9}$

13^9

$13^{-18}$

13^3

Correct answer:

$13^{-9}$

Explanation:

When dividing exponents, we need to make sure we have the same base. In this case we do. Then we just subtract the exponents. Since we are subtracting a positive value, the sign becomes negative. We treat the expression as addition but the answer is negative. The answer is $13^{-3-(6)}=13^{-3-6}=13^{-9}$ .

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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 #133 : Exponents

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

Possible Answers:

$3^{19}$

$3^{60}$

$3^{29}$

27^7

3^7

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 #133 : Exponential Operations

Simplify:

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

Possible Answers:

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

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

None of the other responses gives a correct answer.

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

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

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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SAT Math : Exponential Operations

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #131 : Exponents

Example Question #131 : Exponential Operations

Example Question #133 : Exponential Operations

Example Question #132 : Exponential Operations

Example Question #135 : Exponential Operations

Example Question #22 : How To Divide Exponents

Example Question #133 : Exponents

Example Question #138 : Exponential Operations

Example Question #139 : Exponential Operations

Example Question #133 : Exponential Operations

All SAT Math Resources

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