Laws of exponents formulas

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.

Laws of exponents

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 314 and read as 3 power 14 or 3 raised to the power 14. In 314 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:

♦ ap  x aq = ap+q

Example:

42 x 46 = 42+6  = 48

♦ If ap = aq then p = q

Example:

If 135 = 13p then p = 5

♦ ap / aq = ap-q  if p is greater than q

♦ ap / aq = 1/aq-p if q is greater than p

Example:

79 / 73 = 79-3  = 76

♦ (ap)q = apxq

Example:

(53)7 = 53×7 = 535

Laws of exponents

♦ a0 = 1 ( a is not equal to zero that means other than zero we need to take in the place of a)

Example:

540 =1 , 90 = 1, 6580 = 1,…………

♦ (a/b)p = ap / bp

Example:

(3/7)9 = 39/79

♦ (a x b)p = ap x bp

Example:

(2 x 9)3 = 23 x 93

♦ a-p = 1/ap

Example:

6-4 = 1/64

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

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