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SAT Math : Exponential Operations

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Example Questions

Example Question #31 : Exponential Operations

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

Possible Answers:

$3^{20}+2$

$3^{21}$

3^5-9

3^9

$3^{15}-2$

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 : Exponential Operations

6^7*6^8*6^9

Possible Answers:

$6^{65}$

$6^{-8}$

$6^{24}$

$6^{504}$

$6^{-1}$

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 : Exponential Operations

9^5*9^4*9^0

Possible Answers:

9^9

9^8

9^1

$9^{20}$

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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Example Question #34 : Exponential Operations

$10^{-19}*10^{-17}$

Possible Answers:

$10^{-36}$

$10^{-323}$

10^2

$10^{-2}$

$10^{323}$

Correct answer:

$10^{-36}$

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.

We have two negative values so we treat as a regular addition problem.

The answer is $10^{-19-17}=10^{-36}$ .

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Example Question #36 : Exponents

$14^{-3}*14^{6}$

Possible Answers:

$14^{-18}$

$14^{3}$

$14^{-3}$

$14^{18}$

$14^{9}$

Correct answer:

$14^{3}$

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 positive so our answer must be positive. We treat the equation as a subtraction problem.

The answer is $14^{-3+6}=14^{3}$ .

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Example Question #37 : Exponents

$2^{-9}*2^{-8}*2^{19}*2^{-3}$

Possible Answers:

$2^{-180}$

$2^{180}$

$2^{-39}$

$2^{-1}$

Correct answer:

$2^{-1}$

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. We can add all the negatie values which turns out to be . is greater than and is negative so our answer must be negative.

We treat the equation as a subtraction problem.

The answer is $2^{-20+19}=2^{-1}$ .

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Example Question #38 : Exponents

Simplify.

3^3*2^3*6^3

Possible Answers:

6^9

6^6

Can't be simplified.

$36^{6}$

$36^{9}$

Correct answer:

6^6

Explanation:

Although they have different bases, we can still simplify this expression. To get a base of , we need a base of and . Those are two numbers that give us a base of . In order to change bases, both and bases must be raised to the same exponent. In this case they are. We can say 3^3*2^3 is the same as 6^3 .

Now we have the same base, we can just add the exponents.

The answer is $6^{3+3}=6^6$ .

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Example Question #39 : Exponents

Simplify.

$4^{10}*2^{28}$

Possible Answers:

$8^{280}$

$4^{48}$

$2^{48}$

$2^{38}$

$8^{48}$

Correct answer:

$2^{48}$

Explanation:

Although we have different bases, we can convert base into base . is 2^2 . So for every we will always have 2^2 . We can set-up a proportion.

$\frac{1}{2}=\frac{10}{x}$ .

The top is power raised from base of . The bottom is power raised from base of . So now we cross multiply to get . So now we have same base with different powers. We can add the exponents.

The answer is $2^{20+28}=2^{48}$ .

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Example Question #31 : Exponential Operations

Simplify.

$3^{24}*27^3$

Possible Answers:

$3^{11}$

$27^{33}$

Can't be simplified.

$3^{30}$

$27^{11}$

Correct answer:

$27^{11}$

Explanation:

Although we have different bases, is basically 3*3*3 or 3^3 .

We can set-up a proportion.

$\frac{1}{3}=\frac{x}{24}$

The top is the power raised from a base of . The bottom is the power raised from a base of . When we cross-multiply and divide both sides by , we get . So now we have a base of with different exponents.

We can add them up to get

$27^{8+3}=27^{11}$ .

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SAT Math : Exponential Operations

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #31 : Exponential Operations

Example Question #32 : Exponential Operations

Example Question #33 : Exponential Operations

Example Question #34 : Exponents

Example Question #34 : Exponential Operations

Example Question #36 : Exponents

Example Question #37 : Exponents

Example Question #38 : Exponents

Example Question #39 : Exponents

Example Question #31 : Exponential Operations

All SAT Math Resources

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