Posted by: catindiaonline | October 25, 2008



As you should know from GCSE, x3 is a shortening of x \times x \times x. In the same way, any number to the power of n is that number multiplied by itself n times. To describe more detail, in the expression x3, the x is referred to as the base, and the 3 as the exponent.

By always reducing the expression back to its basic parts it is possible to come to conclusions about how to treat numbers raised to powers in algebra.


When you multiply indices you add the exponents together.

As you can see x^3 \times x^2 = x^{3+2} = x^5 .


Division is, as expected, the opposite to multiplication. When you divide indices you subtract the exponents from each other.

 \frac{x^4}{x^2} = \frac{x \times x \times x \times x}{x \times x} = \frac{\not \! x \times \not \! x \times x\times x}{\not \! x \times \not \! x} = x \times x = x^2

Again this shows that \frac{x^4}{x^2} = x^{4-2} = x^2

Negative powers

Having done the above division, we begin to ask ourselves what happens when we have a fraction that has a higher exponent on the bottom than the top.

Using the trusted method of showing each x seperately we obtain:

For rest go to CAT India Online’s CATclub


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