Exponents

Exponents are numbers that are the superscript of a base number (see figure 1.0). Without fancy notations int can be written like this: a^b with a being the base, ^ indicating that the number after is an exponent, and hence, b being the exponent itself. Exponents tell us how many times we have to multiply the base number by itself. For instance:

22 = 2×2 = 4

23 = 2×2×2 = 8

24= 2×2×2×2 = 16

In many cases, it is essential and recommended to learn a few of these by head, so you know instantly what the answer is if you take a look at an exponent, especially on IB exams. 

Exponential numbers can also be multiplied together. Then, if the base is the same, you only need to add the exponents together and keep the base the same. For instance:

(22) × (24) = 26  = 64

since 2 + 4 is 6.

for division, it is the opposite, where the exponents have to be subtracted from each other. For instance:

(45) / (43) = 42 = 16

If the bases are not the same, but the exponents are, simply rewrite your equation. For instance:

(32) × (52) = (3 × 5)2

Then multiply together the numbers inside the brackets and take the result to the power of the exponent it is taken to:

152 = 225

The Power of a Power Rule will be important in many cases. Let's say we have:

(23)5

This might seem complicated at first, especially if we have larger numbers, but the trick here is to multiply the two exponents together. So:

215 = 32768

There are more to consider, but the rest can be seen in figure 1.1, where you can see all the laws of exponents.