Exponents

Help Questions

ACT Math › Exponents

Questions 1 - 10
1

Which of the following is the square of ?

You may assume both and are positive.

Explanation

Use the square of a sum pattern, substituting for and for in the pattern:

or

2

If an account has interest compounded quarterly at an annual rate of , what is the balance of the account after years of compounding if the initial balance is ? Round to the nearest cent.

Explanation

Recall that the equation for compounded interest (with quarterly compounding) is:

Where is the balance, is the rate of interest, is the number of years, and is the number of times it is compounded per year.

Thus, for our data, we need to know:

This is approximately .

3

If , then

Cannot be determined

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.

4

What is the value of m where:

-2

1

2

4

6

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.

5

can be written as which of the following?

A.

B.

C.

A, B and C

B and C

A and C

C only

B only

Explanation

C is computing the exponent, while A and B are equivalent due to properties of fractional exponents.

Remember that...

6

Simplify the following:

Explanation

When two variables with exponents are multiplied, you can simplify the expression by adding the exponents together. In this particular problem, the correct answer is found by adding the exponents 5 and 5, yielding .

7

can be written as which of the following?

A.

B.

C.

A, B and C

B and C

A and C

C only

B only

Explanation

C is computing the exponent, while A and B are equivalent due to properties of fractional exponents.

Remember that...

8

Which of the following is the square of ?

You may assume both and are positive.

Explanation

Use the square of a sum pattern, substituting for and for in the pattern:

or

9

If an account has interest compounded quarterly at an annual rate of , what is the balance of the account after years of compounding if the initial balance is ? Round to the nearest cent.

Explanation

Recall that the equation for compounded interest (with quarterly compounding) is:

Where is the balance, is the rate of interest, is the number of years, and is the number of times it is compounded per year.

Thus, for our data, we need to know:

This is approximately .

10

Solve for :

Explanation

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

Plugging back into the equation-

Using the formula

We can reduce our equation to

So,

Page 1 of 67