# Help with Exponent Expression

• Aug 17th 2008, 06:11 AM
cmf0106
Help with Exponent Expression
I am going to post the entire problem & its solution. I am confused with one particular step in working towards the solution.

$\displaystyle (2x^3+4)^{-6}(2x^3+4)^4=(2x^3+4)^{-6+4} =(2x^3+4)^{-2} = \frac{1}{(2x^3+4)^2}$

How are the two "$\displaystyle (2x^3+4)$" combined to form one $\displaystyle (2x^3+4)$? Is it because they both have the same base therefore just add the exponents together? Im thinking that must be correct, otherwise I wouldnt be adding these exponents to begin with.
• Aug 17th 2008, 07:31 AM
masters
Quote:

Originally Posted by cmf0106
I am going to post the entire problem & its solution. I am confused with one particular step in working towards the solution.

$\displaystyle (2x^3+4)^{-6}(2x^3+4)^4=(2x^3+4)^{-6+4} =(2x^3+4)^{-2} = \frac{1}{(2x^3+4)^2}$

How are the two "$\displaystyle (2x^3+4)$" combined to form one $\displaystyle (2x^3+4)$? Is it because they both have the same base therefore just add the exponents together? Im thinking that must be correct, otherwise I wouldnt be adding these exponents to begin with.

Remember this rule of exponents:

$\displaystyle x^a \cdot x^b = x^{a+b}$

This explains:

$\displaystyle (2x^3+4)^{-6}(2x^3+4)^4=(2x^3+4)^{-6+4}$

And then, simply add the exponents-6+4 to get:

$\displaystyle (2x^3+4)^{-2}$

And finally, use the reciprocol of the above to reach the conclusion with a positive exponent:

$\displaystyle \frac{1}{(2x^3+4)^2}$