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How do you simplify #(a^7b^5c^8)/(a^5bc^7)#?

Answer 1

Kennedy Adams

See a solution process below:

First, use this rule of exponents to rewrite the #b# denominator:

#a = a^color(red)(1)#

#(a^7b^5c^8)/(a^5b^color(red)(1)c^7)#

Next, use this rule of exponents to eliminate the denominators:

#x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#

#(a^color(red)(7)b^color(red)(5)c^color(red)(8))/(a^color(blue)(5)b^color(blue)(1)c^color(blue)(7)) = a^(color(red)(7)-color(blue)(5))b^(color(red)(5)-color(blue)(1))c^(color(red)(8)-color(blue)(7)) = a^2b^4c^1#

Now, use this rule of exponents to simplify the #c# term:

#a^color(red)(1) = a#

#a^2b^4c#

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Answer 2

Genesis Allen

To simplify the expression (a^7b^5c^8)/(a^5bc^7), divide the coefficients and then subtract the exponents of the variables with the same base. This gives you:

(a^7b^5c^8)/(a^5bc^7) = (a^(7-5)b^(5-1)c^(8-7)) = a^2b^4c

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.