In algebraic expression x^{m}, x is the base and m is the exponent. For all positive number of x except x=1, if an equation contain x^{m} = x^{n} then it will be only possible when m = n.
Here are basic rules of Exponents:
 If a number raised to the power zero then it should be equal to 1.
x^{0} = 1
Example:
2^{0} = 1
 A negative exponent is the same as the reciprocal of the positive exponent.
x^{m} = 1/x^{m}
Example:
2^{4} = 1/2^{4} = 1/16
 If two powers have the same base then we can multiply the powers. When we multiply two powers we add their exponents.
(x^{m}) (x^{n}) = x^{m+n}
Example:
(2^{3})(2^{4}) = 2^{7} = 128
 If two powers have the same base then we can divide the powers. When we divide powers we subtract their exponents.
x^{m}/x^{n} = x^{mn} = 1/x^{nm}
Example:
3^{4}/3^{2} = 3^{2} = 9
 If two powers have different base but same exponent then we multiply the base of powers and exponent will remain same.
(x^{m})(y^{m}) = (xy)^{m}
Example:
3^{2}4^{2} = 12^{2} = 144
 If base is a fraction then the exponent of the power multiply with numerator and denominator separately.
(x/y)^{m} = x^{m}/y^{m}
Example:
(2/3)^{2} = 2^{2}/3^{2} = 4/9
 If power has an exponent then both the exponents multiplied.
(x^{m})^{n} = x^{mn}
Example:
(3^{2})^{3} = 3^{6} = 729
Avoid the common mistakes like below:

x^{m}y^{n} ≠ (xy)^{m+n}
Here bases are not same so we cannot add the exponents.

(x^{m})^{n} ≠ x^{m}x^{n}
Here exponents should be multiplied not added according to rule.

(x + y)^{m} ≠ x^{m} + y^{m}
Have a look at (x + y)^{2} = x^{2} + 2xy + y^{2}
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