Multiplication, division and powers of exponents

Last updated: 11 Nov 2008

Often when a mathematical expression contains more than one exponent it is possible to simplify it.

Multiplication of exponents

If you multiply two exponents with the same base then you simply have to add two exponents. for example,

5 times itself twice times 5 times itself 4 times is 5 times itself 6 times.

We can generalise this to

Division of exponents

You can do a very similar operation to simplify the division of exponents that have the same base. This time, instead of adding the two exponents, you subtract them. For example,

...and more generally,

Exponents of exponents

You can also simplify an exponent of an exponent, this time you multiply the exponents. For example, 2 to the power of 3 all to the power of 4,

Again we can generalise to

Different Bases

You cannot use the rules of multiplication and division with exponents which have different bases. For example,

The first exponent has the base 3 and the other 5, so you cannot simplify the expression.

However, if one of the bases is a power of the other, you can transform them into an expression where they have a common base. For example,

In this case,

Therefore you can replace the 8 in the original expression with

And we know that we can simplify powers of exponents my multiplying them

Which gives us two exponents to multiply with the same base

And that's all you need to know about exponents for the GMAT.

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