Question

410 match the expression with its simplified form using quotient law
\\(\frac{12b^6}{3b^2}\\) \\(4b\\) \\(\frac{16y^3x^3}{2x^2y^2}\\) \\(\frac{22x^6y^7}{11x^2y^3}\\) \\(\frac{18m^3n}{3mn}\\)
\\(\frac{20b^3a}{5ab^2}\\) \\(6m^2\\) \\(2x^4y^4\\)
\\(2m^2\\) \\(\frac{10m^5}{5m^3}\\) \\(8xy\\) \\(4b^4\\) \\(\frac{24a^5b^8}{12a^4b}\\) \\(2ab^7\\)

Explanation:

Step1: Simplify \(\frac{12b^{6}}{3b^{2}}\)

Divide the coefficients and subtract exponents of like bases: \(\frac{12}{3}b^{6 - 2}=4b^{4}\)

Step2: Simplify \(\frac{20b^{3}a}{5ab^{2}}\)

Divide coefficients and subtract exponents: \(\frac{20}{5}b^{3 - 2}a^{1 - 1}=4b\)

Step3: Simplify \(\frac{10m^{5}}{5m^{3}}\)

Divide coefficients and subtract exponents: \(\frac{10}{5}m^{5 - 3}=2m^{2}\)

Step4: Simplify \(\frac{16y^{3}x^{3}}{2x^{2}y^{2}}\)

Divide coefficients and subtract exponents: \(\frac{16}{2}x^{3 - 2}y^{3 - 2}=8xy\)

Step5: Simplify \(\frac{22x^{6}y^{7}}{11x^{2}y^{3}}\)

Divide coefficients and subtract exponents: \(\frac{22}{11}x^{6 - 2}y^{7 - 3}=2x^{4}y^{4}\)

Step6: Simplify \(\frac{18m^{3}n}{3mn}\)

Divide coefficients and subtract exponents: \(\frac{18}{3}m^{3 - 1}n^{1 - 1}=6m^{2}\)

Step7: Simplify \(\frac{24a^{5}b^{8}}{12a^{4}b}\)

Divide coefficients and subtract exponents: \(\frac{24}{12}a^{5 - 4}b^{8 - 1}=2ab^{7}\)

Answer:

• \(\frac{12b^{6}}{3b^{2}}\) matches \(4b^{4}\)
• \(\frac{20b^{3}a}{5ab^{2}}\) matches \(4b\)
• \(\frac{10m^{5}}{5m^{3}}\) matches \(2m^{2}\)
• \(\frac{16y^{3}x^{3}}{2x^{2}y^{2}}\) matches \(8xy\)
• \(\frac{22x^{6}y^{7}}{11x^{2}y^{3}}\) matches \(2x^{4}y^{4}\)
• \(\frac{18m^{3}n}{3mn}\) matches \(6m^{2}\)
• \(\frac{24a^{5}b^{8}}{12a^{4}b}\) matches \(2ab^{7}\)