Notes for Exponents and Powers

(i) x^{m} × x^{n} = x^{m + n}

(ii) x^{m} ÷ x^{n} = x^{m – n}

(iii) x^{m} × b^{m} = (x^{b})^{m}

(ii) x^{0} = 1

When we write 54, it means 5 × 5 × 5 × 5, i.e. 5 is multiplied 4 times. So 5 is the base and 4 is the exponent. We read 54 as �5 raised to the power 4�.

We also know the following laws of exponents

(i) x^{m} × x^{n} = x^{m + n}

(ii) x^{m} ÷ x^{n} = x^{m – n}

(iii) x^{m})^{n} = x^{m × n}

(iv) x^{m} × y^{m} = (xy)^{m}

The value of any number raised to 0 is 1, i.e. a^{0} = 1.

We express very small or very large numbers in standard form (i.e scientific notation) for example:

For a non-zero integer x, we have

or x^{�m} × x^{m} = 1

So x^{�m} is the reciprocal (or the multiplicative inverse) of x^{m} and vice versa.

For example: (i) Reciprocal of 8^{�7} = 8^{7} and

(ii) Reciprocal of 8^{7} = 8^{�7}