Help with Exponent Expression

**cmf0106** · August 17th 2008, 06:11 AM

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

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

How are the two " $(2x^3+4)$ " combined to form one $(2x^3+4)$ ? 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.

**masters** · August 17th 2008, 07:31 AM

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.

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

How are the two " $(2x^3+4)$ " combined to form one $(2x^3+4)$ ? 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:

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

This explains:

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

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

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

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

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

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