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.

Answer

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

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

Answer

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

 

We can’t simplify this, the letters have to be the same!!!!