Question

new: simplify. your answer should contain only positive exponents. simplificar. tu respuesta debe contener sólo exponentes positivos.

1. \\(\frac{2x^2}{x^4}\\)
2. \\(\frac{4x}{x^4}\\)
3. \\(\frac{2m^2}{4m^2}\\)
4. \\(\frac{4x^3}{3x^2}\\)
5. \\(\frac{2a^2b^3}{3ba^2}\\)
6. \\(\frac{2xy^4}{4x^4y^2}\\)

Explanation:

Problem 3: $\boldsymbol{\frac{2x^2}{x^4}}$

Step1: Use exponent rule $\frac{a^m}{a^n}=a^{m - n}$

$\frac{2x^2}{x^4}=2\times x^{2-4}$

Step2: Simplify the exponent

$2\times x^{-2}=\frac{2}{x^2}$ (using $a^{-n}=\frac{1}{a^n}$ to make exponent positive)

Step1: Apply exponent rule $\frac{a^m}{a^n}=a^{m - n}$

$\frac{4x}{x^4}=4\times x^{1 - 4}$

Step2: Simplify the exponent

$4\times x^{-3}=\frac{4}{x^3}$ (using $a^{-n}=\frac{1}{a^n}$)

Step1: Simplify the coefficients and use exponent rule $\frac{a^m}{a^n}=a^{m - n}$

$\frac{2}{4}\times\frac{m^2}{m^2}=\frac{1}{2}\times m^{2-2}$

Step2: Simplify the exponent

$\frac{1}{2}\times m^{0}=\frac{1}{2}\times1=\frac{1}{2}$ (since $a^0 = 1$ for $a
eq0$)

Answer:

$\frac{2}{x^2}$

Problem 4: $\boldsymbol{\frac{4x}{x^4}}$