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Keymaster
Post count: 802

Simplify $$\frac{{6{x^{\frac{3}{2}}}{y^{\frac{1}{2}}} \times {x^{\frac{4}{5}y\frac{3}{5}}}}}{{2{{\left( {{x^{\frac{1}{2}}}y} \right)}^{\frac{1}{5}}} \times 3{x^{\frac{1}{2}}}{y^{\frac{1}{5}}}}}$$

$$= \frac{{6{x^{\frac{{23}}{{10}}}}{y^{\frac{{11}}{{10}}}}}}{{6{x^{\frac{1}{{10}}}}{y^{\frac{1}{5}}} \times {x^{\frac{1}{2}}}{y^{\frac{1}{5}}}}}$$

$$= \frac{{{x^{\frac{{23}}{{10}}}}{y^{\frac{{11}}{{10}}}}}}{{{x^{\frac{3}{5}}}{y^{\frac{2}{5}}}}}$$

$$= {x^{\frac{{17}}{{10}}}}{y^{\frac{7}{{10}}}}$$

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Keymaster
Post count: 802

Simplify $${\left( {\frac{{2{m^3}{n^2}}}{{3m{n^5}}}} \right)^3} \times \frac{{6{m^2}{n^4}}}{{4{m^3}{n^{10}}}}$$

$$= \frac{{8{m^9}{n^6}}}{{27{m^3}{n^{15}}}} \times \frac{{6{m^2}{n^4}}}{{4{m^3}{n^{10}}}}$$

$$= \frac{{4{m^{11}}{n^{10}}}}{{9{m^6}{n^{25}}}}$$

$$= \frac{{4{m^5}}}{{9{n^{15}}}}$$

Keymaster
Post count: 802

Simplify $${\left( {\frac{{2{m^3}{n^2}}}{{3m{n^5}}}} \right)^3} \times \frac{{6{m^2}{n^4}}}{{4{m^3}{n^{10}}}}$$

$$= \frac{{8{m^9}{n^6}}}{{27{m^3}{n^{15}}}} \times \frac{{6{m^2}{n^4}}}{{4{m^3}{n^{10}}}}$$

$$= \frac{{4{m^{11}}{n^{10}}}}{{9{m^6}{n^{25}}}}$$

$$= \frac{{4{m^5}}}{{9{n^{15}}}}$$

Keymaster
Post count: 802

Simplify $$\frac{{7{a^2}b^4}}{{3{a^6}{b^7}}} \div {\left( {\frac{{3ab}}{{2{a^6}{b^4}}}} \right)^3}$$

$$\frac{7}{{3{a^4}{b^3}}} \div \frac{{27{a^3}{b^3}}}{{8{a^{18}}{b^{12}}}}$$

$$= \frac{7}{{3{a^4}{b^3}}} \times \frac{{8{a^{18}}{b^{12}}}}{{27{a^3}{b^3}}}$$

$$= \frac{7}{{3{a^4}{b^3}}} \times \frac{{8{a^{15}}{b^9}}}{{27}}$$

$$=\frac{{56{a^{11}}{b^6}}}{{81}}$$