**Exponentiation** is a mathematical operation, written as **a**** ^{n}**, involving two numbers, the

**base**

*a*and the

**exponent**

*n*. When

*n*is a positive integer, exponentiation is repeated multiplication of the base: that is,

*a*

*is the product of multiplying*

^{n}*n*bases:

And we have,

*a*^{0}= 1*a¹ = a**a² = a x a**a³ = a x a x a**a*(^{n}= a x a x a …. a x a*a*is multiplied*n*times)

Here case, *a** ^{n}* is called the

*n*-th power of

*a*, or

*a*raised to the power

*n*.

Some common exponents have their own names:

- Exponent 2 is called the
*square*of*a*(*a*^{2}) or*a**Square* *E*xponent 3 is called the*cube*of*a*(*a*^{3}) or*a**cubed.*- Exponent −1 of
*a*, or 1 /*a*, is called the*reciprocal*of*a*.

**POINTS TO REMEMBER:**

0

^{n}= 0 for n > 0; 0^{n}is not defined for n ≤ 0a

^{m}= a^{n }if and only if m = n for any a ≠ 0, 1 or -1For any a ≠ 0, and natural number n, a

^{-n}= 1/a^{n}For any a ≠ 0, and integers m, n, a

^{m}x a^{n}= a^{m+n}For any a ≠ 0, and integers m, n, (a

^{m})^{ n}= a^{mn}For any a ≠ 0, b ≠ 0 and integers m, (ab)

^{m}= a^{m }x b^{m}

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