ACT Math : How to multiply exponents

Study concepts, example questions & explanations for ACT Math

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Example Questions

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Example Question #1 : How To Multiply Exponents

Solve: 5x2 – 3y1 where x = 4, y = 5.

 

Possible Answers:

95

65

60

17

Correct answer:

65

Explanation:

Substitute the values for x and y within the equation: 5(4)2 - 3(5)1. Proceed according to proper order of operations: 5(16) – 3(5). Therefore: 80-15= 65.

 

 

Example Question #1 : Exponents

If 64t+1 = (√2)10t + 4, what is the value of t?

Possible Answers:

–1/3

–4

4

1/2

1/3

Correct answer:

–4

Explanation:

In order to set the exponents equal to each other and solve for t, there must be the same number raised to those exponents.

64 = (√2)n?

(√2)2 = 2 and 26 = 64, so ((√2)2)6= (√2)2*6 = (√2)12.

Thus, we now have (√2)12(t+1) = (√2)10t + 4.

12(t+1) = 10t + 4

12t + 12 = 10t + 4

2t + 12 = 4

2t = –8

t = –4

Example Question #3 : How To Multiply Exponents

Evaluate 

(x3)2

Possible Answers:

x4

x9

x6

x5

x23

Correct answer:

x6

Explanation:

You can simplify it into (x3)(x3) = x6

Example Question #2 : Exponents

Simplify: 

Possible Answers:

Correct answer:

Explanation:

To tackle this problem we must understand the concept of exponents in fractions and how to cancel and move them.

 

To move any variable or number from the numerator to the denominator or vice versa, you must negate the exponent. i.e.  in the numerator would become  in the denominator. These two expression are equivalent. You should strive to make all exponents positive initially before applying the next rule to simplify.

Cancelling variables with a similar base is an easy way to simplify. Add or subtract the exponents depending on their relationship in a fraction.

Ex.  or 1.

Ex.  . --> this can be more easily understood if you break down the which then can be moved around to form, . After the  cancels to form 1, we have  or just . This can be applied for all numerical or abstract values of exponents for a given variable, such as or .

Knowing these rules, we can tackle the problem.

To begin we will pick a variable to start with, thereby breaking down the problem into three smaller chunks. First we will start with the variable . . Because the numerator has a negative exponent, we will move it down to the denominator: . This simplifies to  as multiplying any common variables with exponents is found by addition of the exponents atop the original variable. The  variable part of this problem is .

We move to the  section of the problem: . This is similar to our  above, instead with larger numerical exponents. . The  section cancels, leaving us with  or .

Now to the  section. We simply have  on top. Applying the first rule above, we just move it to the denominator with the switching of the sign. Our result is .

Combining all the sections together we have .

More beautifully written it looks like .

Example Question #5 : How To Multiply Exponents

Simplify ((x²)-2)-3

 

Possible Answers:

x4

x-12

x-3

x12

Correct answer:

x12

Explanation:

We are given an expression with a power to a power to a power. Using rules of exponents, we take the exponents and multiply each of them together. 

 

Example Question #6 : How To Multiply Exponents

 What is  (23 )2 ?

 

Possible Answers:

128

64

16

32

Correct answer:

64

Explanation:

Using the rules of exponents,  (23 )2  becomes 26  which is 64.

 

Example Question #3 : Exponents

Find the value of x where:

Possible Answers:

Correct answer:

Explanation:

 

Example Question #3 : How To Multiply Exponents

Which of the following is equivalent to:

 

Possible Answers:

Correct answer:

Explanation:

The first step is to distribute the squared on the second term. (2a3)2 becomes 4a6 by multiplying the exponents (power raised to a power exponent rule) and squaring the 2.  Then, combining like terms (i.e. combining coefficients, a's and b's) we obtain 12a8b5.

Example Question #5 : How To Multiply Exponents

Simplify the following expression:

 (3y2)2 + (4y)3

 

Possible Answers:

81y4 + 64y3

73y12

73y7

9y4 + 64y3

None of the above

Correct answer:

9y4 + 64y3

Explanation:

This requires us to remember the rules for multiplying and adding exponent variables.

 

(3y2)2 can be re-written as (3)2 x (y2)2 which yields 9y4

 

(4y)3 can be re-written as (4)3 x (y)3 which yields 64y3

 

adding the two yields

 

9y4 +64y3

Example Question #6 : How To Multiply Exponents

Simplify the following expression:

Possible Answers:

Correct answer:

Explanation:

The answer is (x10)/2. When an exponent is raised to another power, you multiply the exponents.

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