Learn the important **laws of exponents** formulas. **Exponents** are also called as **indices** and also called as **power**. In exponents and powers chapter we have mainly **eight laws of exponents (indices) formulas**. Each and every single formula is very important in exponents chapter.

Let us consider the product 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3. If we observe the product we can able to see that we multiplied 3, 14 times. So the entire product we can write it as 3^{14} and read as **3 power 14 or 3 raised to the power 14**. In 3^{14} notation 3 is called as base and 14 is called as **exponent**. 14 is also called as power and also called as index. Now we will the laws of **exponents formulas**.

**List of laws of exponents (indices) explained with an example:**

♦ a^{p } x a^{q} = a^{p+q}

Example:

4^{2} x 4^{6} = 4^{2+6 } = 4^{8}

♦ If a^{p} = a^{q} then p = q

Example:

If 13^{5} = 13^{p} then p = 5

♦ a^{p} / a^{q} = a^{p-q} if p is greater than q

♦ a^{p} / a^{q} = 1/a^{q-p} if q is greater than p

Example:

7^{9} / 7^{3} = 7^{9-3 } = 7^{6}

♦ (a^{p})^{q} = a^{pxq}

Example:

(5^{3})^{7} = 5^{3×7} = 5^{35}

♦ a^{0} = 1 ( a is not equal to zero that means other than zero we need to take in the place of a)

Example:

54^{0} =1 , 9^{0} = 1, 658^{0} = 1,…………

♦ (a/b)^{p} = a^{p} / b^{p}

Example:

(3/7)^{9} = 3^{9}/7^{9}

♦ (a x b)^{p} = a^{p} x b^{p}

Example:

(2 x 9)^{3} = 2^{3} x 9^{3}

♦ a^{-p} = 1/a^{p}

Example:

6^{-4} = 1/6^{4}

Learning and remembering these **eight laws of exponents (indices) formulas** will be helpful.

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