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ACT Math : How to add exponents

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Example Question #1 : How To Add Exponents

For all x, 2x² times 12x³ equals...

Possible Answers:

14x⁵

14x⁶

24x⁶

24x⁵

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 #31 : Exponential Operations

Multiply: 2x² * 3x

Possible Answers:

6x³

5x³

2x³

6x²

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 #32 : Exponential Operations

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 x 10³

1.08

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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Example Question #1 : How To Add Exponents

Simplify: hⁿ + h^–2n

Possible Answers:

$h^{-n}$

Correct answer:

Explanation:

h^–2n= 1/h²ⁿ

hⁿ + h^–2n= hⁿ + 1/h²ⁿ

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Example Question #1 : How To Add Exponents

Simplify: 3y² + 7y² + 9y³ – y³ + y

Possible Answers:

19y¹¹

10y² + 9y³

10y⁴ + 8y⁶ + y

10y² + 10y³ + y

10y² + 8y³ + y

Correct answer:

10y² + 8y³ + y

Explanation:

Add the coefficients of similar variables (y, y², 9y³)

3y² + 7y² + 9y³ – y³ + y =

(3 + 7)y² + (9 – 1)y³ + y =

10y² + 8y³ + y

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Example Question #3 : How To Add Exponents

Simplify the following:

$\frac{K^3K^4}{M^6M^2}$

Possible Answers:

$\frac{K^8}{M^7}$

$\frac{K^{12}}{M^{12}}$

$\frac{K^{-1}}{M^4}$

$\frac{KM^{\frac{1}{2}}}{KM^{\frac{1}{2}}}$

$\frac{K^7}{M^8}$

Correct answer:

$\frac{K^7}{M^8}$

Explanation:

When common variables have exponents that are multiplied, their exponents are added. So K³* K⁴ =K⁽³⁺⁴⁾ = K⁷. And M⁶ * M² = M⁽⁶⁺²⁾ = M⁸. So the answer is K⁷/M⁸.

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Example Question #9 : How To Add Exponents

Solve for :

$\frac{64^4}{8^x} = 8$

Possible Answers:

x=8

x=1

x=-7

x=7

x=0

Correct answer:

x=7

Explanation:

First, reduce all values to a common base using properties of exponents.

64^4 = (8^2)^4 = 8^8

Plugging back into the equation-

$8^8 = 8^x\cdot 8^1$

Using the formula

$x^a\cdot x^b=x ^{a+b}$

We can reduce our equation to

x +1 = 8

So,

x = 7

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Example Question #4 : How To Add Exponents

Simplify: y³x⁴(yx³ + y²x² + y¹⁵ + x²²)

Possible Answers:

2x⁴y⁴ + 7y¹⁵ + 7x²²

y⁴x⁷ + y⁵x⁶ + y¹⁸x⁴ + y³x²⁶

y³x¹² + y⁶x⁸ + y⁴⁵ + x⁸⁸

y³x¹² + y¹²x⁸ + y²⁴x⁴ + y³x²³

y³x¹² + y⁶x⁸ + y⁴⁵x⁴ + y³x⁸⁸

Correct answer:

y⁴x⁷ + y⁵x⁶ + y¹⁸x⁴ + y³x²⁶

Explanation:

When you multiply exponents, you add the common bases:

y⁴ x⁷ + y⁵x⁶ + y¹⁸x⁴ + y³x²⁶

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ACT Math : How to add exponents

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : How To Add Exponents

Example Question #31 : Exponential Operations

Example Question #3 : How To Add Exponents

Example Question #32 : Exponential Operations

Example Question #5 : How To Add Exponents

Example Question #1 : How To Add Exponents

Example Question #1 : How To Add Exponents

Example Question #3 : How To Add Exponents

Example Question #9 : How To Add Exponents

Example Question #4 : How To Add Exponents

All ACT Math Resources

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