Evaluate expressions using properties of exponents
Key Notes :
Properties of exponents
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.
Properties of exponents can help to simplify expressions with exponents. The table shows some properties of exponents and examples.
Learn with an example
🔥Evaluate. Write your answer as a whole number or as a simplified fraction.
125 /123 =
To divide powers with the same base, subtract their exponents.
First, combine powers with the same bases.
125 / 123= 125 − 3 —–> Divide the 12’s, remembering to subtract the exponents
= 122
Now evaluate.
122 = 144
🔥Evaluate. Write your answer as a whole number or as a simplified fraction.
42 · 42 =
To multiply powers with the same base, keep the base and add the exponents.
Evaluate.
42 · 42 = 16 · 42 ——->Evaluate 42
= 16 · 16 ———->Evaluate 42
= 256 ——>Multiply
🔥Evaluate. Write your answer as a whole number or as a simplified fraction.
27/24=
First combine powers with the same bases.
27 / 24 = 27-4 —–> Divide the 2’s, remembering to subtract the exponents
= 23
Now evaluate.
23 = 8
Let’s practice!
