Question

standard: rn.a.o2 - rewrite expressions involving radicals and rational exponents using the properties of exponents.

1. simplify \\(\frac{(6x^4)(2x^6)}{4x^2}\\)? show your work or explain your reasoning.

Explanation:

Step1: Simplify the numerator first

First, we have \((6x^{4})(2x^{6})\). Using the property of exponents \(a^m \cdot a^n = a^{m + n}\) and the commutative property of multiplication for the coefficients:
\((6\times2)(x^{4}\times x^{6}) = 12x^{4 + 6}=12x^{10}\)

Step2: Now divide by the denominator \(4x^{2}\)

We have \(\frac{12x^{10}}{4x^{2}}\). Using the property of exponents \(\frac{a^m}{a^n}=a^{m - n}\) for the variables and dividing the coefficients:
For the coefficients: \(\frac{12}{4} = 3\)
For the variables: \(\frac{x^{10}}{x^{2}}=x^{10 - 2}=x^{8}\)
Combining these results, we get \(3x^{8}\)

Answer:

\(3x^{8}\)