ACT Math : Exponential Operations

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #2 : How To Divide Exponents

Simplify:

\small \frac{x^2y^3z^4}{x^3y^4z^2}

Possible Answers:

\small xyz^2

\small \frac{yz^2}{x}

\small \frac{z}{x^2y^2}

\small \frac{z^2}{xy}

Correct answer:

\small \frac{z^2}{xy}

Explanation:

To simply exponents in a fraction, subtract the exponent for each variable in the denominator from the exponent in the numerator. This will leave you with

\small x^{-1}y^{-1}z^2 or \small \frac{z^2}{xy}

Example Question #3 : How To Divide Exponents

What is the value of m where:

 

Possible Answers:

4

2

6

-2

1

Correct answer:

2

Explanation:

If n=4, then 64(4/12)=64(1/3)=4.  Then, 4=mŸ4(1+m)/(m+4). If 2 is substituted for m, then 4=2Ÿ4(1+2)/(2+4)=2Ÿ41/2=2Ÿ√4=2Ÿ2=4.

 

 

Example Question #4 : How To Divide Exponents

Simplify the following:

 

Possible Answers:

1/x4

x4

Cannot be done

x7/3

Correct answer:

x4

Explanation:

These exponents have the same base, x, so they can be divided. To divide them, you take the exponent value in the numerator (the top exponent) and subtract the exponent value of the denominator (the bottom exponent). Here that means we take 7 – 3 so our answer is x4.

Example Question #5 : How To Divide Exponents

Simplify:

Possible Answers:

Correct answer:

Explanation:

Use rule for multiplying exponents to simplify the numerator. 

Use rule for dividing exponents to simplify. 

Example Question #6 : How To Divide Exponents

Simplify:

Possible Answers:

Correct answer:

Explanation:

Simplify:

Step 1: Simplify the fraction. When dividing exponents subtract the exponents on the bottom from the exponents on the top.

Step 2: Distribute the exponent. When raising an exponent to a power, multiply them together.

Example Question #7 : How To Divide Exponents

Simplify

\dpi{100} \small \frac{20x^{4}y^{-3}z^{2}}{5z^{-1}y^{2}x^{2}}=

Possible Answers:

\dpi{100} \small \frac{4x^{2}z^{3}}{y^{5}}

\dpi{100} \small 15x^{2}y^{2}z^{2}

\dpi{100} \small {4x^{5}y^{-2}}

\dpi{100} \small 15x^{-2}y^{-2}z^{-2}

None

Correct answer:

\dpi{100} \small \frac{4x^{2}z^{3}}{y^{5}}

Explanation:

Divide the coefficients and subtract the exponents.

Example Question #8 : How To Divide Exponents

Which of the following is equal to the expression Equationgre, where  

xyz ≠ 0?

Possible Answers:

xy

z/(xy)

1/y

xyz

z

Correct answer:

1/y

Explanation:

(xy)4 can be rewritten as x4y4 and z0 = 1 because a number to the zero power equals 1.  After simplifying, you get 1/y. 

Example Question #9 : How To Divide Exponents

If , then

 

Possible Answers:

Cannot be determined

Correct answer:

Explanation:

Start by simplifying the numerator and denominator separately. In the numerator, (c3)2 is equal to c6. In the denominator, c2 * c4 equals c6 as well. Dividing the numerator by the denominator, c6/c6, gives an answer of 1, because the numerator and the denominator are the equivalent.

 

Example Question #10 : How To Divide Exponents

If , which of the following is equal to ?

Possible Answers:

a

a6

The answer cannot be determined from the above information

a18

a4

Correct answer:

a18

Explanation:

The numerator is simplified to  (by adding the exponents), then cube the result. a24/a6 can then be simplified to .

Example Question #11 : How To Divide Exponents

Simplify the following

.

Possible Answers:

Correct answer:

Explanation:

Start by remembering that you "flip" negative exponents over the division bar, thus moving from the top to the bottom and vice-versa. (There are other ways to do this as well, though most students understand this way most easily.)

Next, you just eliminate common factors and combine on the numerator. First combine the s:

Cancel out the numeric coefficient:

Now eliminate s and s:

 

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