Powers are repeated multiplication.

You can revise your square numbers and cube numbers here.

Practice calculating powers here with Transum.

Expressions involving powers have a base and a power. The base is the big number which is being raised to the power. The power is the small number on the top.

Practice working with powers using the two links above before moving onto learning the algebraic rules of powers (laws of indices).

Note that the words powers and indices mean the same thing.

Multiplying two powers with the same base is the same as writing a single power which is the sum of the two powers.

Look at the example on the left.
We added 3 and 5 to make 8.

Dividing two powers with the same base is the same as writing a single power which is first power minus the second power.

Look at the example on the right. 10 minus 3 is 7.

A power to another power is the same as just multiplying the two powers.

Look at the example on the left. 5 x 6 = 30

Anything to the power of 1 is itself.

It’s the simplest rule!

Anything to the power 0 (zero) is 1.

If you ever see a power of zero, you can immediately simplify the whole thing to be just 1.

A negative power makes a fraction. The numerator is 1 and the denominator is the base to the positive power.

If it is a fraction to a negative power, the fraction flips.

Look at the example on the right.
The power of minus 2 flips the fraction and then squares everything.

The minus sign flips the fraction, then the 2 powers everything by 2.

To begin, let’s look at the power of a half.

The power of a half is the same as a square root.

Now, what is the general rule for fractional powers?

The denominator of the power tells you the root, and the numerator tells you the power.

Transum: True of False Laws of Indices Revision
(try levels 1, 2 and 3)