# Exponents and Powers

## Exponential form is a form involving two numbers written as an, where a is the base and n is the exponent. Powers are a short way which shows, how many times a number is multiplied by itself. In general for any non – zero integer ‘a’, a-m = 1/am, where m = positive integer, a-m is the multiplicative inverse of am. Laws of exponents: (i) am × an = a(m + n) (ii) am ÷ an = a(m - n) (iii) (am)n = amn (iv) am × bm = (ab)m (v) a0 = 1 (vi) am / bm = (a/b)m When a number is multiplied with itself thrice, the product so obtained is called the cube of the number. Consider a number an, where a is any number. Here, n is called the exponent. A mathematical expression an, where a is any number, is called an exponential expression. Powers are a short way which shows, how many types a number is multiplied by itself. When a number is multiplied with itself, the product so obtained is called the square of the number. A number expressed as a decimal number between 1.0 and 10.0 (including 1.0) multiplied by a power of 10 is said to be in standard form. Standard form is also known as scientific notation.

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