 What you need to know

Things to remember:

• “Exponent” is a fancy way of saying “power”.
• Exponents and powers tell us how many times we need to multiply a number by itself.

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.

$$6^2 = 6\times 6$$

$$6^3 = 6\times 6\times 6$$

$$6^4= 6\times 6\times 6\times 3$$

0 a special power, because the answer is always 1!

$$5^0 = 1$$

$$123^0 = 1$$

$$23.4^0 = 1$$

$$\pi^0 = 1$$

What is the value of $5^3$?

$$5^3=5\times5\times5=25\times5=125$$

What is the value of $4^3+2^5$?

$$4^3=4\times4\times4=16\times4=64$$

$$2^5=2\times2\times2 \times2 \times2 =4\times2 \times2 \times2 =8\times2 \times2 =16\times2 =32$$

$$4^3+2^5 =64+32=96$$

Exponent are mainly used to write things in a quicker way, so instead of writing lots of multiplications we can just write it with powers

$$2\times2\times2\times2\times2\times2\times8\times8\times8\times8=2^6\times8^4$$

Powers are also useful for computing. Try typing $\times2$ into your calculator 70 times.

• This is going to take a long time; typing $2^{70}$ is much quicker.
• Your calculator probably doesn’t have enough memory to let you type it 70 times!

Example Questions

$$7\times7\times7\times2\times2\times2\times9\times9\times9$$

$$7^3\times2^3\times9^3$$

$$5^4=5\times5\times5\times5=25\times5\times5=125\times5=625$$

$$3^2=3\times3=9$$

$$5^4\times3^2 =625\times9=5625$$