Math

QuestionSimplify the expression: 12a3b6c53a2b4c5\frac{12 a^{3} b^{6} c^{5}}{3 a^{2} b^{4} c^{5}}

Studdy Solution

STEP 1

Assumptions1. We are given the expression 12a3b6c53ab4c5\frac{12 a^{3} b^{6} c^{5}}{3 a^{} b^{4} c^{5}}. . We need to simplify this expression.

STEP 2

We can simplify the expression by separately simplifying the coefficients, the terms with aa, the terms with bb, and the terms with cc.

STEP 3

First, simplify the coefficients. Divide12 by3.
123=\frac{12}{3} =

STEP 4

Next, simplify the terms with aa. The rule for dividing like bases is to subtract the exponents.a3/a2=a32=a1=aa^{3} / a^{2} = a^{3-2} = a^{1} = a

STEP 5

Then, simplify the terms with bb. Again, subtract the exponents.
b/b4=b4=b2b^{} / b^{4} = b^{-4} = b^{2}

STEP 6

Finally, simplify the terms with cc. The exponents are the same, so c5/c5=1c^{5} / c^{5} =1.

STEP 7

Now, combine all the simplified parts to get the simplified expression.
4a1b21=4ab24a^{1}b^{2}1 =4ab^{2}So, the simplified form of the given expression is 4ab24ab^{2}.

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