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

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

Mathematics
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(4a^5/7b^4) * (2b^2/2a^4)
Rewrite like this: \[\frac{4a^5 \dot\ 2b^2}{2a^4 \dot\ 7b^4}\]

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Other answers:

ok and then?
do i just multiply accross?
Or you can work with each separately by re-writing like this: \[\frac{4}{2} \dot\ \frac{a^5}{a^4} \dot\ \frac{2}{7} \dot\ \frac{b^2}{b^4}\]
so it would be 8ab^7??
for the top part?
No
wow thats confusing o.O
You already know how to reduce the numerical fractions.
You know that 4/2 = 2. You also know that 2/7 is already in simplest form and cannot be reduced any further
mhk
So for the numbers, you are just left with \[2 \times \frac{2}{7} = \frac{4}{7}\]
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^{y-x}}, x
So \[\frac{a^5}{a^4} = a^{5 - 4} = a^1 = a\] \[\frac{b^2}{b^4} = \frac{1}{b^{4-2}} = \frac{1}{b^2}\]
thes are my multiple choice answers: 4a^9/7b^^6 4a/7b^2 7b^2/4a 4/7a^9b^6
\[\frac{4}{7} \times a \times \frac{1}{b^2} = \frac{4a}{7b^2}\]
alirght so B? Thanks! <3
You should learn how to do these on your own.

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