Question

simplify.
\\(\dfrac{28x^{5}y^{2}}{32xy^{2}}\\)

Explanation:

Step1: Simplify coefficients

Find the greatest common divisor (GCD) of 28 and 32. The GCD of 28 and 32 is 4. Divide numerator and denominator by 4:
$\frac{28\div4}{32\div4}=\frac{7}{8}$

Step2: Simplify \(x\)-terms

Use the rule of exponents $\frac{x^m}{x^n}=x^{m - n}$. For \(x\)-terms: $\frac{x^5}{x}=x^{5 - 1}=x^4$

Step3: Simplify \(y\)-terms

Use the rule of exponents $\frac{y^m}{y^n}=y^{m - n}$. For \(y\)-terms: $\frac{y^2}{y^2}=y^{2 - 2}=y^0 = 1$ (since any non - zero number to the power of 0 is 1)

Step4: Combine the results

Multiply the simplified coefficient, \(x\)-term, and \(y\)-term together: $\frac{7}{8}\times x^4\times1=\frac{7x^4}{8}$

Answer:

$\frac{7x^4}{8}$