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

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