**Evaluating Exponents** *KS3 Revision*

## What you need to know

**Things to remember:**

- Counting how many times you do the multiplications can help keep track of how many you have done and how many are left.
- A power of 1 doesn’t change the number
- A power of 0 is always 1.
- 1 to any power is 1.
- 0 to any power is 0.

An exponent is a number written to the top right of a number and tells us how many times we multiply a number by itself.

6^2 = 6\times 6

6^3 = 6\times 6\times 6

6^4= 6\times 6\times 6\times 6

So, all we’re doing when we have exponents is lots of multiplications. When we do these multiplications, we refer to it as “evaluating the exponent”.

*Evaluate the following exponents:*

* *

5^2=5\times5=25

7^3=7\times7\times7=343

8^4=8\times8\times8\times8=4096

* *

There are some special exponents that give some nice easy answers.

**Exponent equals 1**

When the exponent is 1, the answer is the same as what you started with.

5^1=5

27.14^1=27.14

\pi^1=\pi

** **

**Exponent equals 0**

If the exponent is 0, it always equals 1.

5^0=1

27.14^0=1

\pi^0=1

** **

** **

**1 to any power is always 1.**

If we think about 1 to a power, it just means we are multiply 1 by itself lots of times.

1^3=1\times1\times1=1

1^5=1\times1\times1\times1\times1=1

1^12=1

1^{3.5}=1

*Note:** You don’t really need to worry about decimal powers.*

** **

**0 to any power is always 0.**

If we think about 0 to a power, it just means we are multiplying 0 by itself. Whenever we multiply a number by 0, it’s 0.

0^3=0\times0\times0=0

0^5=0\times0\times0\times0\times0=0

0^12=0

0^{3.5}=0

## Example Questions

**Question 1:** Evaluate 3^5

3^5=3\times3\times3\times3\times3=243

**Question 2:** Evaluate 17.89^1

17.89^1=17.89