How do you simplify #\frac { 10t ^ { 4} } { 2t ^ { 4} \cdot t ^ { 7} \cdot t ^ { 3} }#?

1 Answer
smendyka
Dec 18, 2017

See a solution process below:

Explanation:

First, rewrite the expression as:

#(10/2)(t^4/(t^4 * t^7 * t^3)) =>#

#((5 * 2)/2)(t^4/(t^4 * t^7 * t^3))#

Next, cancel common terms in the numerators and denominators:

#((5 * color(blue)(cancel(color(black)(2))))/color(blue)(cancel(color(black)(2))))(color(red)(cancel(color(black)(t^4)))/(color(red)(cancel(color(black)(t^4))) * t^7 * t^3)) =>#

#5(1/(t^7 * t^3)) =>#

#5/(t^7 * t^3)#

Now, use this rule for exponents to simplify the denominator:

#x^color(red)(a) xx x^color(blue)(b) = x^(color(red)(a) + color(blue)(b))#

#5/(t^color(red)(7) * t^color(blue)(3)) =>#

#5/t^(color(red)(7)+color(blue)(3)) =>#

#5/t^10#

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