**HELLO Hiveans**

I will be talking about indices in mathematics today, so many find it difficult but after today, it will be a walkaway topic.

**INDICES**.

Index are an expression of an equation that has a base and power/index.

It is the opposite of a logarithm.

Mathematically:

**LAW OF INDICES**

**Multiplication law of indices:**

This law state that when two or more equation or expression of the same base are joined by a multiplication(×) sign, You take one base and add the powers.

**Mathematically**:

3^(6)× 3^(4)

=3^(6-4)

3^2.

**Division law of indices**:

This law states that when two equations or expressions are joined by the division sign(÷), u takes one base and subtracts the powers.

**Mathematically**:

10^4 ÷10^2= 10^(4-2)

=10^2.

**Zero law of indices**:

This law state that when an equation or expression is raised to a power of zero(0), The resultant answer is zero(0).

NB:if an alphabet or number is raised to a power of zero, it is equal to zero.

**Mathematically**:

10^(0)=0

(A)^(0)=0

(3A)^(0) =0.

**Power law of indices**:

This law states that when an equation or expression is raised to a number, all raised to a power of a certain number, You take the base and multiply the powers.

**Mathematically**:

(2^2)^2= (2)^(2×2)

2^(4)

(2a)^(2)

=4A^2.

**Fraction law of indices**:

This law states that when an expression or equation is raised to the power of a fraction, u takes the denominator as the root and the numerator as the power.

**Mathematically**.

**Example** 1.

Find the expression of the equation below.

(2a)^3 ×(4a)^2

Solution

**Example** 2.

Find the expression on the equation

3^4÷9^3

Solution

Thanks for reading.