 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

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

$$17.89^1=17.89$$