Question

Help really hard please

Answer 1

`\large\boxed{\tt x^{(5)/(6)} + 2x^{(7)/(3)}}`

Explanation:

`\textsf{We are asked to simplify the given expression.}`

`\textsf{We should use the \underline{Distributive Property, and Rule of Multiplying Exponents.}}`

`\boxed{\begin{minipage}{25 em} \underline{\textsf{\large Distributive Property;}} \\ \\ \textsf{Distributive Property is a property that allows us to multiply the term to the left of the parentheses with the terms inside the parentheses.} \\ \\ \underline{\textsf{\large Example;}} \\ \tt a(b+c) = \boxed{\tt ab+ac} \end{minipage}}`

`\boxed{\begin{minipage}{25 em} \underline{\textsf{\large Rule of Multiplying Exponents;}} \\ \\ \textsf{Whenever we have to multiply 2 terms with exponents, it's important to know the Rule of Multiplying Exponents. This rule states that whenever 2 exponential terms multiply together, their exponents add together. }\\ \\ \underline{\textsf{\large Example;}} \\ \tt x^(3) * \tt x^(4) = x^(3+4) = \boxed{\tt x^(7)} \end{minipage}}`

`\large\underline{\textsf{Solving;}}`

`\textsf{We should first use the Distributive Property, then use the Rule of Multiplying}`

`\textsf{Exponents.}`

`\tt x^{(1)/(3)} (x^{(1)/(2)} + 2x^(2))`

`\underline{\textsf{Use the Distributive Property;}}`

`\tt x^{(1)/(3)} (x^{(1)/(2)} + 2x^(2)) = (x^{(1)/(3)} * x^{(1)/(2)}) + (x^{(1)/(3)} * 2x^(2))`

`\underline{\textsf{Use the Rule of Multiplying Exponents;}}`

`\tt (x^{(1)/(3)} * x^{(1)/(2)}) + (x^{(1)/(3)} * 2x^(2)) = x^{(1)/(3) + (1)/(2)} + 2x^{(1)/(3) + (2)/(1) }`

`\underline{\textsf{Find Common Denominators per fractions;}}`

`\tt x^{(1)/(3) + (1)/(2)} + 2x^{(1)/(3) + (2)/(1)} = x^{(2)/(6) + (3)/(6)} + 2x^{(2)/(6) + (12)/(6)}`

`\underline{\textsf{Add;}}`

`\tt x^{(2)/(6) + (3)/(6)} + 2x^{(2)/(6) + (12)/(6)} = x^{(5)/(6)} + 2x^{(14)/(6)`

`\underline{\textsf{Simplify Fractions;}}`

`\large\boxed{\tt x^{(5)/(6)} + 2x^{(7)/(3)}}`