sue101
What is the product in simplest form? State any restrictions on the variable.



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sue101
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(4a^5/7b^4) * (2b^2/2a^4)

sue101
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@Hero

Hero
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Rewrite like this:
\[\frac{4a^5 \dot\ 2b^2}{2a^4 \dot\ 7b^4}\]

sue101
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ok and then?

sue101
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do i just multiply accross?

Hero
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Or you can work with each separately by rewriting like this:
\[\frac{4}{2} \dot\ \frac{a^5}{a^4} \dot\ \frac{2}{7} \dot\ \frac{b^2}{b^4}\]

sue101
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so it would be 8ab^7??

sue101
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for the top part?

Hero
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No

sue101
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wow thats confusing o.O

Hero
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You already know how to reduce the numerical fractions.

Hero
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You know that 4/2 = 2. You also know that 2/7 is already in simplest form and cannot be reduced any further

sue101
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mhk

Hero
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So for the numbers, you are just left with
\[2 \times \frac{2}{7} = \frac{4}{7}\]

Hero
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For the variables, you have to use this rule:
\[\frac{a^y}{a^x} = a^{y  x}, y > x\]
\[\frac{b^x}{b^y} = \frac{1}{b^{yx}}, x<y\]

Hero
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So \[\frac{a^5}{a^4} = a^{5  4} = a^1 = a\]
\[\frac{b^2}{b^4} = \frac{1}{b^{42}} = \frac{1}{b^2}\]

sue101
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thes are my multiple choice answers: 4a^9/7b^^6
4a/7b^2
7b^2/4a
4/7a^9b^6

Hero
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\[\frac{4}{7} \times a \times \frac{1}{b^2} = \frac{4a}{7b^2}\]

sue101
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alirght so B? Thanks! <3

Hero
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You should learn how to do these on your own.