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ACT Math : Exponents

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #31 : Exponents

Simplify: $(y^{3})^{4}$

Possible Answers:

$y^{12}$

$y^{7}$

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

$4y^{3}$

Correct answer:

$y^{12}$

Explanation:

When an exponent is raised to an exponent, multiply the two together to yield a new exponent, and attach that exponent to the original base.

In this case, multiply and to yield , and your answer is $y^{12}$ .

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Example Question #32 : Exponential Operations

Solve: $(x^{2})^{2}$ when x=4 .

Possible Answers:

256

Correct answer:

256

Explanation:

When an exponent is raised to another exponent, you may multiply them together to find the exponent of the answer. Attach that exponent to the original base, and that is the solution.

In this particular problem, multiply by , which yields as the final exponent. This makes $x^{4}$ .

Now, substitute for : $4^{4}=256$ .

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Example Question #2221 : Act Math

What is

$\frac{x^{-1}}{x^{-2}}$ ?

Possible Answers:

$\frac{-1}{x}$

$\frac{-1}{x^{2}}$

x^2

Correct answer:

Explanation:

Negative exponents are reciprocals. Do not change the sign to negative.

The variables with negative exponents can be written as their reciprocals.

$x^{-1} = \frac{1}{x}$

$\frac{1}{x^{-2}} = x^{2}$ ,

Multiplying these new forms together gives,

$x^{2} * \frac{1}{x}=$

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

From here, simplify by factoring out a common factor from the numerator and denominator.

$\frac{x^{2}}{x}=\frac{x\cdot x}{x}=x$

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Example Question #32 : Exponents

Simplify the following:

(xy^3)^2

Possible Answers:

x^3y^5

$\frac{y}{x}$

$\frac{1}{x^2y^6}$

x^2y^6

Correct answer:

x^2y^6

Explanation:

To solve, simply distribute the outer exponent. When you have an exponent to an exponent, you multiply their values. Thus,

$(xy^3)^2=x^{1*2}y^{3*2}=x^2y^6$

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Example Question #2222 : Act Math

Which of the following is a value of x that satisfies

$2^{x+2}\cdot 2^{2x-3}=32$

Possible Answers:

Correct answer:

Explanation:

This question incorporates properties of exponents. The best way to solve this problem is to establish the same base for all of the terms.

$2^{x+2}\cdot 2^{2x-3}=2^{5}$

Now use the properties of exponents to simplify the left side of the equation. When exponential terms with the same base are multiplied, the exponents are added.

$2^{x+2}\cdot 2^{2x-3}=2^{(x+2)+(2x-3)}=2^{3x-1}$

Now, with the left side simplified, set that equal to $2^{5}$ .

$2^{3x-1}=2^{5}$

Since each side has one term with the same base, simply set the exponents equal to each other and solve for x.

3x-1=5

3x=6

x=2

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Example Question #34 : Exponents

For all x, 2x² times 12x³ equals...

Possible Answers:

24x⁶

14x⁶

24x⁵

14x⁵

Correct answer:

24x⁵

Explanation:

You multiply the integers, then add the exponents on the x's, giving you 24x⁵.

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Example Question #1 : How To Add Exponents

Multiply: 2x² * 3x

Possible Answers:

6x²

2x³

6x³

5x³

Correct answer:

6x³

Explanation:

When multiplying exponents you smiply add the exponents.

For 2x² times 3x, 2 times 3 is 6, and 2 + 1 is 3, so 2x² times 3x = 6x³

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Example Question #3 : How To Add Exponents

What is 2³ + 2²?

Possible Answers:

Correct answer:

Explanation:

Using the rules of exponents, 2³ + 2²= 8 + 4 = 12

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Example Question #2 : How To Add Exponents

Solve for where:

$3^{x+1}=9^{x}$

Possible Answers:

Correct answer:

Explanation:

The only value of x where the two equations equal each other is 1. All you have to do is substitute the answer choices in for x.

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Example Question #5 : How To Add Exponents

A particle travels 9 x 10⁷ meters per second in a straight line for 12 x 10^-6 seconds. How many meters has it traveled?

Possible Answers:

1.08 x 10⁵

1.08 x 10

1.08

1.08 x 10³

Correct answer:

1.08 x 10³

Explanation:

Multiplying the two numbers yields 1080. Expressed in scientific notation 1080 is 1.08 x 10³.

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ACT Math : Exponents

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #31 : Exponents

Example Question #32 : Exponential Operations

Example Question #2221 : Act Math

Example Question #32 : Exponents

Example Question #2222 : Act Math

Example Question #34 : Exponents

Example Question #1 : How To Add Exponents

Example Question #3 : How To Add Exponents

Example Question #2 : How To Add Exponents

Example Question #5 : How To Add Exponents

All ACT Math Resources

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