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SAT Math : Exponential Operations

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Example Questions

Example Question #21 : Exponents

If and are positive integers and $2^{2a}(2^{2b})=16$ , what is the value of a +b ?

Possible Answers:

Correct answer:

Explanation:

The question tells us that 2^2a ( 2^2b)= 16.

We can rewrite 16 as 2⁴, giving us 2^2a ( 2^2b)= 2⁴.

When terms with the same base are multipled, their exponents can be added:

2^{(2a +2b)}= 2⁴

Since the base is the same on both sides of the equation, we can equate the exponents:

2a +2b = 4

2(a + b) = 4

a + b = 2

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Example Question #1 : How To Multiply Exponents

(b * b⁴* b⁷)^1/2/(b³ * b^x) = b⁵

If b is not negative then x = ?

Possible Answers:

–1

–2

Correct answer:

–2

Explanation:

Simplifying the equation gives b⁶/(b^3+x) = b⁵.

In order to satisfy this case, x must be equal to –2.

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Example Question #2 : How To Multiply Exponents

If〖7/8〗ⁿ= √(〖7/8〗⁵),then what is the value of n?

Possible Answers:

¹/₅

√5

⁵/₂

²/₅

Correct answer:

⁵/₂

Explanation:

7/8 is being raised to the 5th power and to the ¹/₂ power at the same time. We multiply these to find n.

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Example Question #4 : How To Multiply Exponents

Simplify: (x³ * 2x⁴ * 5y + 4y² + 3y²)/y

Possible Answers:

10x⁷ + 7y

10x¹¹ + 7y³

10x⁷ + 7y³

None of the other answers

10x⁷y + 7y²

Correct answer:

10x⁷ + 7y

Explanation:

Let's do each of these separately:

x³ * 2x⁴ * 5y = 2 * 5 * x³* x⁴* y = 10 * x⁷ * y = 10x⁷y

4y² + 3y² = 7y²

Now, rewrite what we have so far:

(10x⁷y + 7y²)/y

There are several options for reducing this. Remember that when we divide, we can "distribute" the denominator through to each member. That means we can rewrite this as:

(10x⁷y)/y + (7y²)/y

Subtract the y exponents values in each term to get:

10x⁷ + 7y

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Example Question #21 : Exponential Operations

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.

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

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

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 #7 : How To Multiply Exponents

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

Possible Answers:

$25^{29}$

$5^{40}$

$5^{180}$

$5^{29}$

$25^{180}$

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 #8 : How To Multiply Exponents

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

Possible Answers:

$210^{7}$

$30^{14}$

$30^{49}$

$77^{7}$

$12^{49}$

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:

$12x^{2}$

$432x^{3}$

$6x^{2}$

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 #23 : Exponents

Evaluate:

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

Possible Answers:

$\dpi{100} \small 24$

$\dpi{100} \small 30$

$\dpi{100} \small 78$

$\dpi{100} \small 81$

$\dpi{100} \small 27$

Correct answer:

$\dpi{100} \small 78$

Explanation:

Can be simplified to:

Capture2

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Example Question #24 : How To Multiply Exponents

2^3*2^4

Possible Answers:

$2^{12}$

2^4-3

2^3*3

2^1

2^7

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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SAT Math : Exponential Operations

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #21 : Exponents

Example Question #1 : How To Multiply Exponents

Example Question #2 : How To Multiply Exponents

Example Question #4 : How To Multiply Exponents

Example Question #21 : Exponential Operations

Example Question #7 : How To Multiply Exponents

Example Question #8 : How To Multiply Exponents

Example Question #22 : Exponential Operations

Example Question #23 : Exponents

Example Question #24 : How To Multiply Exponents

All SAT Math Resources

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