Question

calculate the area of a triangle with base (6a^{3}b^{3}c^{12}) and height (3ab^{8}c^{4}).

Explanation:

Step1: Recall the formula for the area of a triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\).

Step2: Substitute the given values of base and height into the formula

Here, base \(b = 6a^{3}b^{3}c^{12}\) and height \(h=3ab^{8}c^{4}\). So, \(A=\frac{1}{2}\times(6a^{3}b^{3}c^{12})\times(3ab^{8}c^{4})\).

Step3: Simplify the expression

First, multiply the coefficients: \(\frac{1}{2}\times6\times3 = 9\).
Then, use the rule of exponents \(x^{m}\times x^{n}=x^{m + n}\) for the variables:
For \(a\): \(a^{3}\times a=a^{3 + 1}=a^{4}\).
For \(b\): \(b^{3}\times b^{8}=b^{3+8}=b^{11}\).
For \(c\): \(c^{12}\times c^{4}=c^{12 + 4}=c^{16}\).

So, \(A = 9a^{4}b^{11}c^{16}\).

Answer:

\(9a^{4}b^{11}c^{16}\)