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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 power to the power rule states that 'If the base raised to a power is being raised to another power, then the two powers are multiplied and the base remains the same.' The formula for the power of a power rule is (a m ) n = a m n .
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.
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:
The power of a power rule is an important exponent rule (law of exponent) used to simplify an expression of the form (x m) n, where the base x is raised to a power m and the entire expression x m is raised to the power n again. Power raised to a power rule is given by. (x m) n = x m × n = x m n …where x is the base, m and n are exponents.
Exponents formulas refer to the formulas that help solve exponents. Exponent of a number is represented in the form: x n, meaning x is multiplied by itself for n times. Here, x is called the "base". n is called the "exponent" or "power". x n is read as "x to the power of n" (or) "x raised to n".
Power of a Power: (a m) n = a mn; Power of a Product: (ab) m = a m b m; Power of a Quotient: (a/b) m = a m /b m; What is the Purpose of the Exponent Rules? The purpose of exponent rules is to simplify the exponential expressions in fewer steps.
