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

Question 1: Write the following using powers:

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

Answer

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

 

7^3\times2^3\times9^3

Question 2: What is the value of 5^4\times3^2?

Answer

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

 

3^2=3\times3=9

 

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