Laws of Exponents

An exponent is a mathematical notation that represents how many times a base is multiplied by itself. Other terms used to define exponents are ‘power’ or ‘index’. An exponential term is a term that can be expressed as a base raised to an exponent. For example, in an exponential expression an, 'a' is the base and ‘n' is the exponent.

The exponents can be numbers or constants; they can also be variables. Exponents are generally positive real numbers, but they can also be negative numbers.

Laws of exponents:

If a and b are any real numbers, and m and n are rational numbers then,

  •  am × an = am+n

  •  a m a n = am-n, m > n.

  • (am)n = amn

  • (am × bm) = (a × b)m

  • a m b m = ( a b )m

  • a0 = 1

  • a-n = 1 a n

Summary

An exponent is a mathematical notation that represents how many times a base is multiplied by itself. Other terms used to define exponents are ‘power’ or ‘index’. An exponential term is a term that can be expressed as a base raised to an exponent. For example, in an exponential expression an, 'a' is the base and ‘n' is the exponent.

The exponents can be numbers or constants; they can also be variables. Exponents are generally positive real numbers, but they can also be negative numbers.

Laws of exponents:

If a and b are any real numbers, and m and n are rational numbers then,

  •  am × an = am+n

  •  a m a n = am-n, m > n.

  • (am)n = amn

  • (am × bm) = (a × b)m

  • a m b m = ( a b )m

  • a0 = 1

  • a-n = 1 a n

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