1.6 G) Multiplication & Division with Negative Powers
- When we are multiplying powers with the same base, we add the powers.
- When we are dividing powers with the same base, we take the powers.
With negative powers, we need to be really careful with the signs.
Example 1
What is:
The bases are the same (both of them are y) and we are multiplying, which means that we will be adding the powers.
The adding of a negative number results in us taking that number.
The answer is y3.
Example 2
What is:
The bases are the same (both of them are f) and we are dividing, which means that we are going to be taking the powers away from one another.
The answer is f-7.
Example 3
What is:
The bases are both g and we are dividing, so we are going to be taking powers.
The subtracting of a negative number results in us adding the number. Therefore, – -6 becomes + 6.
The answer is g11.
Raising a Power to Another Power
We are now going to have an example of raising a power to another power. When we raise a power to another power, we multiply the powers.
Example 4
What is:
We are raising a power to another power, so we multiply the powers.
A negative number multiply by a positive number results in a negative. Therefore, -4 x 7 is -28; the power is -28.
The answer is h-28.