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# Multiplying Exponents

The exponents are the numbers or variables which are raised to either constants or variables. Exponentiation of a variable is defined as its repeated multiplication. The number of times a number or variable is multiplied to itself is raised as its power and is called exponent. Exponents are illustrated in the following figure: Exponent are defined as:
$x^{y}$ = x * x * x *.....* x (y times)

Multiplying Exponents

In order to multiply two exponents, following properties of exponents are to be used :

• When two exponents on the same base are multiplied together, their exponents are added on the same base, such as : $x^{m}.x^{n}=x^{m+n}$
• When exponent is raised to another exponents, the exponent are multiplied on the given base, i.e. $(x^{m})^{n}=x^{(mn)}$
• When same exponents on different base are multiplied together, their bases are multiplied and raised by given exponent, such as : $x^{m}.y^{m}=(xy)^{m}$

Let us understand above rules with the help of examples.

Example 1: Solve $3^{2}.2^{2}$.
Solution: $3^{2}.2^{2}$
= $(3*2)^{2}$
= $6^{2}$
= 36

Example 2: Simplify $(-3a^{2}b).(2abc).(a^{3}b^{5}(c^{2})^{2})$.
Solution: $(-3a^{2}b).(2abc).(a^{3}b^{5}(c^{2})^{2})$
= $-6.a^{(2+1+3)}.b^{(1+1+5)}.c.c^{4}$
= $-6a^{6}b^{7}c^{(1+4)}$
= $-6a^{6}b^{7}c^{5}$

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