# So what are exponents? Let's find out

So **what are exponents**? Exponents can be considered a shortcut method for replacing repetitive multiplication. Suppose you want to multiply 'a' with itself 'b' number of times, then its effective to write it as a^{b} instead of a x a x a ...(b times). This method of representing repeated product is called exponentiation as per the **definition of exponents. **Exponents help solve some of the math problems very easily.

## Use of exponentiation in math:

** **Exponentiation can be used in day to day math problems. They can be applied in any of the daily problems also. In the expression a^{b}, 'a' can be called the base while 'b' is the exponent. According to the **exponents definition**, a^{b} implies 'a' being multiplied 'b' number of times. The computer memory addressing is an best example of the use of exponents. We represent it in the power of 2. Say for example 1024 bits can be represented by notation 2^{10}.

If we want to multiply two exponential forms with each other having the same base, then this can be done by simply changing the exponent value to sum of exponents according to the **definition of exponent. **Note that this rule applies only for exponents with same base. Consider that we want a product of a^{b} and a^{c}. Then the finalized expression can be written as a^{b+c}. Couple of examples will make this concept stand clear.

(1) Find the value of 2^{5}:

We know that 2^{5} means multiplying 2 with itself 5 times. This can be done as 2 x 2 x 2 x 2 x 2 = 32. Thus 2^{5} equals 32.

(2) Write 256 as the power of 2:

if we multiply 2 with itself 8 number of times, we get 256. Thus the exponent is 8 and the answer is 2^{8}.

(3) Find the product of 3^{4} x 3^{-2}:

The exponents gets added if the base are same. Here we need to subtract them as one of it is negative. Hence 3^{4} x 3^{-2} = 3^{4-2} = 3^{2} = 9. Thus the answer is 9.

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