Question

simplify the expression below. \\(\frac{-10x^{3}y^{3}z^{7}}{5x^{5}y^{3}z^{6}}\\)

Explanation:

Step1: Simplify the coefficients

Divide the coefficient of the numerator (-10) by the coefficient of the denominator (5): $\frac{-10}{5} = -2$

Step2: Simplify the \(x\)-terms

Using the rule of exponents $\frac{a^m}{a^n} = a^{m - n}$, for the \(x\)-terms: $\frac{x^3}{x^5} = x^{3 - 5} = x^{-2}=\frac{1}{x^2}$

Step3: Simplify the \(y\)-terms

For the \(y\)-terms: $\frac{y^3}{y^3} = y^{3 - 3} = y^0 = 1$ (since any non - zero number to the power of 0 is 1)

Step4: Simplify the \(z\)-terms

For the \(z\)-terms: $\frac{z^7}{z^6}=z^{7 - 6}=z^1 = z$

Step5: Combine all the simplified terms

Multiply the simplified coefficient, \(x\)-term, \(y\)-term, and \(z\)-term together: $-2\times\frac{1}{x^2}\times1\times z=\frac{-2z}{x^2}$

Answer:

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