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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] .
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:
Exponent Rules. Exponent rules are those laws that are used for simplifying expressions with exponents. Many arithmetic operations like addition, subtraction, multiplication, and division can be conveniently performed in quick steps using the laws of exponents.
Power of a power. We can raise exponential to another power, or take a power of a power. The result is a single exponential where the power is the product of the original exponents: (xa)b = xab. We can see this result by writing it as a product where the xa is repeated b times: (xa)b = xa × xa × ⋯ × xa ⏟ b times.
The power of a power rule in exponents is a rule that is applied to simplify an algebraic expression when a base is raised to a power, and then the whole expression is raised to another power. Before we get into the detail of the concept, let us recall the meaning of power and base.
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.
What Is the Power of a Power Rule? 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.
