I need help with Product-to-Exponent/Same-Base

J

justdillwithit

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May 23, 2006
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Suppose I have a problem in which I need to use both the product-to-exponent along with the same-base product rule. What steps would I use to simplify expressions like these:

(wx)^3 w^-4 x^7

or

(wx)^4 x^-7
-----------------
w^3 (wx)^-2

I understand how to solve equations by just using these rules individually, my problem is I don't understand how to combine them properly. I know that I have to work out the product-to-exponent rule first, but what do I do next?
 
Evaluate terms in parentheses first. Then add exponents for like bases.
 
justdillwithit said:
Suppose I have a problem in which I need to use both the product-to-exponent along with the same-base product rule. What steps would I use to simplify expressions like these:

(wx)^3 w^-4 x^7

or

(wx)^4 x^-7
-----------------
w^3 (wx)^-2

I understand how to solve equations by just using these rules individually, my problem is I don't understand how to combine them properly. I know that I have to work out the product-to-exponent rule first, but what do I do next?
Click to expand...

First: apply the ^3 to variables inside the parentheses, so that you obtain
w^3x^3 times w^(-4)x^7

Now apply the rule that when multiplying you add the exponents of a base variable.
w^3*w^(-4) = w^(3-4) = w^(-1) (* stands for multiplication; it's used here to emphasize we have terms that are still to be multiplied, since writing expressions with exponents using a keyboard isn't as clear as when handwritten)

the x^3 * x^(-7) would be multiplied similarly.
 
TATOO this to the inside of your left hand:

x^a times x^b = x^(a+b) [1]
x^(-a) = 1 / x^a [2]

Apply that to your equation: (wx)^3 w^-4 x^7

Since (wx)^3 = w^3 x^3 , then:

w^3 x^3 w^(-4) x^7

w^(3-4) x^(3+7) : see rule [1]
w^(-1) x^10

x^10 / w : see rule [2]
 
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