Identify equivalent expressions involving exponents

Key Notes :

An exponent shows repeated multiplication of a base.

For example, in the expression x4, x is the base and 4 is the exponent. You can expand the expression by using the base, x, as a factor four times.

x4=x.x.x.x

You can refer to an exponent expression such as x4 as a power.

Use Properties of exponents to Identify equivalent expressions involving exponents

Learn with an example

Select all the expressions that are equivalent to 85,3-3

  • 1/8-9
  • 8-9
  • 8
  • 80

To find which expressions are equivalent to 83.8-3, write each expression with the same base.

The answer choices and 83 . 8 –3 can all be written as a power of 8. So, use properties of exponents to write each expression in the form 8 ( ). Then, see which ones match 83 . 8 –3 in this form.

Step 1: Write 83.8–3 in the form 8( )

83.8–3

= 83+-3 Use the identity axay = ax+y

= 80

A positive number raised to zeroth power is 1. So, 83 . 8-3  is equal to 1.

Step 2: Now see which expressions are also equal to 80 = 1.

See if 1 / 8-9 is equal to 1.

1 / 8-9

=8-(-9) Use the identity 1/ax=a–x

= 89

So, 1 / 8-9 is equal to 89, but 83 . 8-3 is not. (It is equal to 80=1.)
The expressions1 / 8-9and 83 . 8-3are not equivalent.

The expression 8-9 is in the form 8 . You’ve already found that 83 . 8-3 is not equal to 8-9 (It is equal to 80=1)

The expression 8-9 and  83 . 8-3 are not equivalent.

8 is not equal to 1 , but 83 . 8-3 is equal to 1

The expression 8 and 83 . 8-3 are not equivalent.

you’ve already found 83 . 8-3 is equal to 80 .

The expression 80 and  83 . 8-3 are equivalent.

The correct answer is 80.

Select all the expressions that are equivalent to (103)0.

  • 10
  • 1/100
  • 1
  • 1/103

To find which expressions are equivalent to (103)0, write each expression with the same base.

The answer choices and (103)0 can all be written as a power of 10. So, use properties of exponents to write each expression in the form 10 ( )
. Then, see which ones match (103)0 in this form.

Step 1: Write (103)0 in the form 10.

(103)0

= 103.0 Use the identity (ax)y=axy

=100

A positive number raised to zero power is 1. So, (103)0 is equal to 1.

Step 2: Now see which expressions are also equal to 100=1.

10 is not equal to 1, but (103)0 is equal to 1.

The expressions 10 and (103)0 are not equivalent.

See if 1/100 is equal to 1.

1/100

1/1 Use the identity a0=1

1

Both 1/100 and (103)0 are equal to 1.

The expressions 1/100 and (103)0 are equivalent.

You’ve already found that (103)0 is equal to 1.
The expressions 1 and (103)0 are equivalent.

See if 1/103 is equal to 1.

1/103

=10–3

Use the identity
1/ax=a–x

So, 1/103 is equal to 10–3, but (103)0 is not. (It is equal to 100=1.)
The expressions 1/103 and (103)0 are not equivalent.

The correct answers are:

=1/100

=1

Let’s practice!