This Crash Course is a review of the laws of exponents covered in Secondary 3, but which are used again in Secondary 4 and 5.
To understand this video, you will need to be familiar with exponential notation and the following vocabulary: base, exponent, power and root. Understanding the order of operations and fractions will also help you understand this video.
To help apply the laws of exponents, it is helpful to understand the powers of prime numbers and the powers of 10.
Before applying most exponent laws, it's important to ensure that the bases are the same.
Here is a summary of the laws of exponents and an example for each property:
|
Name of the property |
Explanation |
Example |
|---|---|---|
|
Multiplying powers with the same base |
The exponents are added. |
|2^{5} \times 2^{-1} \times 2^{3} =2^{7}| |
|
Dividing powers with the same base |
The exponents are subtracted. |
|\dfrac{5^{8}}{5^{2}} = 5^{6}| |
|
Power of a power |
The exponents are multiplied. |
|\left(x^{2}\right)^{7} = x^{14}| |
|
Power of a product |
An exponent can be distributed when it is applied to a bracket that contains a multiplication. |
|\left(3ab\right)^{7} = 3^7a^7b^7| |
|
Power of a quotient |
An exponent can be distributed when it is applied to a bracket that contains a division. |
|\left(\dfrac{2}{3}\right)^{5} = \dfrac{2^5}{3^5}| |
|
Power of a negative exponent |
When an exponent is negative, the numerator and denominator must be inverted to make it positive. |
|z^{-4} = \dfrac{1}{z^4}| |
|
Power of a fractional exponent |
A fractional exponent can always be expressed as a root. |
|c^{^\frac{2}{3}}= \sqrt[3]{c^2}| |
|
Special case |
If two powers of the same base are equal, the exponents are equal. |
|7^{2} = 7^{x}| if and only if |2 = x| |