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In mathematics, exponentiation is an operation involving two numbers: the base and the exponent or power. Exponentiation is written as bn, where b is the base and n is the power; often said as " b to the power n ". [1] .
Basic rules for exponentiation. If n is a positive integer and x is any real number, then xn corresponds to repeated multiplication. xn = x × x × ⋯ × x n times. We can call this “ x raised to the power of n,” “ x to the power of n,” or simply “ x to the n.”. Here, x is the base and n is the exponent or the power.
The exponent of a number says how many times to use the number in a multiplication. In words: 8 2 could be called "8 to the power 2" or "8 to the second power", or simply "8 squared". Exponents make it easier to write and use many multiplications. Example: 96 is easier to write and read than 9 × 9 × 9 × 9 × 9 × 9.
Laws of Exponents. Exponents are also called Powers or Indices. The exponent of a number says how many times to use the number in a multiplication. In this example: 82 = 8 × 8 = 64. In words: 8 2 could be called "8 to the second power", "8 to the power 2" or simply "8 squared". Try it yourself:
Exponents and powers are ways used to represent very large numbers or very small numbers in a simplified manner. For example, if we have to show 3 x 3 x 3 x 3 in a simple way, then we can write it as 3 4, where 4 is the exponent and 3 is the base. The whole expression 3 4 is said to be power.
The power (or exponent) of a number says how many times to use the number in a multiplication. It is written as a small number to the right and above the base number. In this example the little "2" says to use 8 two times in a multiplication: 8 2 = 8 × 8 = 64.
Power of a power property: ( xm )n = xm × n. Power of a product property: (xy)m = xmym. Power of a quotient property: \small { \left (\dfrac {x} {y}\right)^ {\mathrm {m}} = \dfrac {x^ {\mathrm {m}}} {y^ {\mathrm {m}}} } (yx )m = ymxm . Quotient property: \small { \dfrac {x^ {\mathrm {m}}} {x^ {\mathrm {n}}} = x^ {\mathrm { {m-n}}} } xnxm =xm−n.
