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SAT Math : Exponents

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Example Questions

Example Question #21 : How To Add Exponents

Evaluate 3^7+3^7+3^7

Possible Answers:

$3^{10}$

$3^{21}$

3^8

$3^{27}$

$3^{14}$

Correct answer:

3^8

Explanation:

When adding exponents, we don't multiply the exponents but we try to factor to see if we simplify the addition problem. In this case, we can simplify it by factoring 3^7 . We get 3^7(1+1+1)=3^7(3)=3^8 .

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Example Question #91 : Exponents

Evaluate 5^7+5^7+5^7+5^7+5^7

Possible Answers:

$5^{60}$

$5^{35}$

5^8

$5^{40}$

5^9

Correct answer:

5^8

Explanation:

When adding exponents, we don't multiply the exponents but we try to factor to see if we simplify the addition problem. In this case, we can simplify it by factoring 5^7 . We get 5^7(1+1+1+1+1)=5^7(5)=5^8 .

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Example Question #23 : How To Add Exponents

Evaluate $2^{12}+4^6$

Possible Answers:

$2^{15}(3)$

4^7(3)

$2^{13}$

$2^{12}(5)$

$4^{12}$

Correct answer:

$2^{13}$

Explanation:

Although we have different bases, we do know 4=2^2 . Therefore our expression is $2^{12}+(2^2)^6=2^{12}+2^{12}$ . Remember to apply the power rule of exponents. Then, now we can factor $2^{12}$ . $2^{12}+2^{12}=2^{12}(1+1)=2^{12}(2)=2^{13}$

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Example Question #23 : How To Add Exponents

If $\dpi{100} \small r$ and $\dpi{100} \small s$ are positive integers, and $\dpi{100} \small 25\left ( 5^{r} \right )=5^{s-2}$ , then what is $\dpi{100} \small s$ in terms of $\dpi{100} \small r$ ?

Possible Answers:

$\dpi{100} \small r+4$

$\dpi{100} \small r+1$

$\dpi{100} \small r$

$\dpi{100} \small r+2$

$\dpi{100} \small r+3$

Correct answer:

$\dpi{100} \small r+4$

Explanation:

$\dpi{100} \small 25\left ( 5^{r} \right )$ is equal to $5^{2}\left ( 5^{r}\right )$ which is equal to $\dpi{100} \small \left ( 5^{r+2} \right )$ . If we compare this to the original equation we get $\dpi{100} \small r+2=s-2\rightarrow s=r+4$

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Example Question #25 : How To Add Exponents

Evaluate:

2^8+2^8

Possible Answers:

2^7

4^8

$2^{16}$

$2^{15}$

2^9

Correct answer:

2^9

Explanation:

When adding exponents, you want to factor out to make solving the question easier.

2^8+2^8 we can factor out 2^8 to get

2^8(1+1)=2^8(2) .

We have the same base so we just apply the exponent rule for multiplication to get

$2^8(2)=2^{8+1}=2^9$ .

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Example Question #26 : How To Add Exponents

Which of the following is equivalent to $16^6+4^{12}+64^{4}+256^3$ ?

Possible Answers:

256^4

16^8

64^3

$4^{13}$

$4^{14}$

Correct answer:

$4^{13}$

Explanation:

Although each base is different, we can convert them to a common base of

We know

$16^6=(4^2)^6=4^{12}$ ,

$64^4=(4^3)^4=4^{12}$ ,

and

$256^3=(4^4)^3=4^{12}$ .

Remember to apply the power rule of exponents.

Therefore we have

$4^{12}+4^{12}+4^{12}+4^{12}$ .

We can factor out $4^{12}$ to get

$4^{12}(1+1+1+1)=4^{12}(4)=4^{13}$ .

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Example Question #27 : How To Add Exponents

Simplify: $3^{2x}+3^{2x}+3^{2x}$

Possible Answers:

$3^{3x+1}$

$3^{2x}$

$3^{6x}$

$3^{3x}$

$3^{2x+1}$

Correct answer:

$3^{2x+1}$

Explanation:

When adding exponents, you want to factor out to make solving the question easier.

$3^{2x}+3^{2x}+3^{2x}$

We can factor out $3^{2x}$ to get

$3^{2x}(1+1+1)=3^{2x}*3$ .

Now we can add exponents and therefore our answer is

$3^{2x+1}$ .

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Example Question #92 : Exponents

Given $9 \cdot 3^n = 3^9$ , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

Express as a power of ; that is: 9=3^2 .

Then $3^2 \cdot 3^n = 3^9$ .

Using the properties of exponents, $3^{n+2}=3^9$ .

Therefore, n+2=9 , so n=7 .

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Example Question #93 : Exponents

If $9^{(x + 5)}+3^{2(x+5)}=162$ , what is the value of ?

Possible Answers:

Correct answer:

Explanation:

Since we have two ’s in $9^{(x + 5)} + 3^{2(x + 5)}$ we will need to combine the two terms.

For $3^{2(x + 5) }$ this can be rewritten as

$(3^2)^{ (x + 5)} = 9^ {(x + 5)}$

So we have $9^{ (x + 5) }+ 9^{ (x + 5)} = 162$ .

Or $2 (9^{ (x + 5)}) = 162$

Divide this by : $9^{ (x + 5)} = 81 = 9^ 2$

Thus x +5 = 2 or x = -3

*Hint: If you are really unsure, you could have plugged in the numbers and found that the first choice worked in the equation.

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Example Question #13 : Exponents

If m and n are integers such that m < n < 0 and m² – n² = 7, which of the following can be the value of m + n?

I. –5

II. –7

III. –9

Possible Answers:

II and III only

II only

I, II and III only

I only

I and II only

Correct answer:

II only

Explanation:

m and n are both less than zero and thus negative integers, giving us m² and n² as perfect squares. The only perfect squares with a difference of 7 is 16 – 9, therefore m = –4 and n = –3.

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SAT Math : Exponents

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #21 : How To Add Exponents

Example Question #91 : Exponents

Example Question #23 : How To Add Exponents

Example Question #23 : How To Add Exponents

Example Question #25 : How To Add Exponents

Example Question #26 : How To Add Exponents

Example Question #27 : How To Add Exponents

Example Question #92 : Exponents

Example Question #93 : Exponents

Example Question #13 : Exponents

All SAT Math Resources

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