1. What are Indices?
"An index, also known as an exponent, is a small number that appears after a number or letter to indicate how many times that number or letter has been multiplied by itself.
For example, 5² = 5 × 5 = 25
2. What are the Laws of Indices?
The laws of indices, also known as the rules of exponents. Understanding and applying these laws is crucial for solving many types of math problems on your GCSE exam.
Let's go over each of the indices laws individually.
2.1 Multiplication Law:
The law of multiplication for indices states that when multiplying indices with the same base, the result is the base raised to the sum of the powers.
This law can be written as follows:
aˆm × aˆn = aˆm+n
Examples:
3ˆ3 × 3ˆ6 = 3ˆ3+6 = 3ˆ9
6ˆ8 × 6ˆ-5 = 6ˆ8-5 = 6ˆ3
2.2 Division Law:
The law of division for indices states that when dividing indices with the same base, the result is the base raised to the difference of the powers.
This law can be written as follows:
aˆm ÷ aˆn = aˆm-n
Examples:
5ˆ6 ÷ 5ˆ4 = 5ˆ6-4 = 5ˆ2
2ˆ9 ÷ 2ˆ4 = 2ˆ9-4 = 2ˆ5
2.3 Brackets with Indices Law
The law of brackets with indices states that when there is a power outside the bracket, multiply the powers.
This law is as follows:
(aˆm)ˆn = aˆm×n
Examples:
(7ˆ2)ˆ3 = 7ˆ2×3 = 7ˆ6
(5ˆ5)ˆ2 = 5ˆ5×2 = 5ˆ10
2.4 Power of Zero Law
The law of indices for the power of zero states that any base raised to the power of 0 is equal to 1.
This law is as follows:
aº = 1
Examples:
5º = 1
7º = 1
2.5 Negative Indices Law
The law of negative indices states that when a base is raised to a negative exponent, the result is the reciprocal of the base raised to a positive exponent.
This law is as follows:
aˆ-m = 1⁄aˆm
Examples:
2ˆ-3 = 1⁄2ˆ3= 1⁄8
5ˆ-2 = 1⁄5ˆ2= 1⁄25
2.6 Fractional Indices Law
The law of fractional indices states that when the power is a fraction, the denominator will be the root of the number or letter, then raise the answer to the power of the numerator.
This law is as follows:
aˆm⁄n = (n√a)ˆm
Examples:
16ˆ¾ = (4√16)³ = (2)³ = 8
27ˆ2⁄3 = (3√27)² = (3)² = 9
