What you need to know

Things to remember:

• When multiplying terms with the same base number, we just need to add the exponents together.
• We don’t write the exponent if it is just 1.

“Exponents” is just another way of saying “powers”, and tells us how many times we have to multiply a number or letter by itself.

$$3^4=3\times3\times3\times3$$

$$5^6=5\times5 \times5 \times5 \times5 \times5$$

$$a^2=a\times a$$

$$n^5=n\times n\times n\times n\times n$$

Simplify $3^3\times3^2$ by writing as one power.

We know that exponents are just a quick way of writing lots of multiplications, so let’s write this in the long way to start with:

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

So, really, this is just lots of multiply by 3. How many 3s do we have here? 5. So we can write this as:

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

$$3^3\times3^2=3^5$$

Interesting, if we look at the powers, we can see that they just added together!

$$3+2=5$$

So, all we have to do is add the powers together!

Note: The numbers/letters before the powers have to be the same!!!

$$4^5\times4^7=4^{5+7}=4^{12}$$

$$3^5\times3^5=3^{5+5}=3^{10}$$

$$c^1\times c^2=c^{1+2}=c^{3}$$

$$a^11\times a^{-3}=1^{11+-3}=1^8$$

Example Questions

Question 1: Simplify $2^9\times2^11$ by writing as a one power.

$$2^9\times2^11=2^{9+11}=2^{20}$$

Question 2: Simplify $a^4\times x^5$ by writing as a one power.

$$a^4\times x^5= a^4\times x^5$$