EDEXCEL GCSE FOUNDATION MATHS - What are Laws of Indices

Laws of Indices

The laws of indices are a set of rules that help us simplify expressions involving exponents (powers). Here are the main laws:

1. Multiplication:

• When multiplying powers with the same base, add the exponents.

x^m * x^n = x^(m+n)

Example: x^3 * x^5 = x^(3+5) = x^8

2. Division:

• When dividing powers with the same base, subtract the exponents.

x^m / x^n = x^(m-n)

Example: x^7 / x^2 = x^(7-2) = x^5

3. Power of a Power:

• When raising a power to another power, multiply the exponents.

(x^m)^n = x^(m*n)

Example: (x^4)^3 = x^(4*3) = x^12

4. Zero Exponent:

• Any non-zero number raised to the power of zero equals 1.

x^0 = 1 (x ? 0)

Example: 5^0 = 1

5. Negative Exponent:

• A number raised to a negative exponent is equal to its reciprocal with a positive exponent.

x^-n = 1/x^n (x ? 0)

Example: x^-3 = 1/x^3

6. Fractional Exponent:

• A fractional exponent represents a root.

x^(m/n) = (n?x)^m

Example: x^(2/3) = (?x)^2

Examples:

1. Simplify: (2x^3)^4 * x^2
2. Applying the power of a power rule: (2x^3)^4 = 2^4 * x^(3*4) = 16x^12

3. Applying the multiplication rule: 16x^12 * x^2 = 16x^(12+2) = 16x^14

4. Simplify: x^5 / x^-2

5. Applying the division rule: x^5 / x^-2 = x^(5-(-2)) = x^7

Important Notes:

• These laws only work for powers with the same base.
• Remember that the laws of indices can be applied to simplify complex expressions.
• Practice using the laws regularly to build your understanding and confidence.