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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:
For the expression b x, b is the base and x is the power (also called the exponent) which implies b is multiplied by itself x times. Now, the power of a power rule is used to simplify expressions of the form (b x) y which on simplification is written as b xy.
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 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.
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. (4) 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.
Exponent rules are those laws that are used for simplifying expressions with exponents. Learn about exponent rules, the zero rule of exponent, the negative rule of exponent, the product rule of exponent, and the quotient rule of exponent with the solved examples, and practice questions.
Exponents. The exponent of a number says how many times to use the number in a multiplication. In 82 the "2" says to use 8 twice in a multiplication, so 82 = 8 × 8 = 64. In words: 8 2 could be called "8 to the power 2" or "8 to the second power", or simply "8 squared".
