Question 74288
*[Tex \LARGE \frac{\sqrt{42a^3b^5}}{\sqrt{14a^2b}}]
*[Tex \LARGE \frac{\sqrt{42}\sqrt{a^3}\sqrt{b^5}}{\sqrt{14}\sqrt{a^2}\sqrt{b}}]Rewrite square roots using the identity: *[Tex \LARGE \sqrt{xyz}=\sqrt{x}\sqrt{y}\sqrt{z}]
*[Tex \LARGE \frac{\sqrt{42}(a^3)^{\frac{1}{2}}(b^5)^{\frac{1}{2}}}{\sqrt{14}(a^2)^{\frac{1}{2}}(b)^{\frac{1}{2}}}] Rewrite square roots into powers (ie *[Tex \LARGE \sqrt(x)=x^{\frac{1}{2}] or in more general terms *[Tex \LARGE \sqrt[n](x)=x^{\frac{1}{n}]
*[Tex \LARGE \frac{\sqrt{42}(a^{3*\frac{1}{2}})(b^{5*\frac{1}{2}})}{\sqrt{14}(a^{2*\frac{1}{2}})(b^{\frac{1}{2}})}] Multiply the exponents

*[Tex \LARGE \frac{\sqrt{42}(a^{\frac{3}{2}})(b^{\frac{5}{2}})}{\sqrt{14}(a^{1})(b^{\frac{1}{2}})]hello
*[Tex \LARGE \frac{\sqrt{42}(a^{\frac{3}{2}-1})(b^{\frac{5}{2}-\frac{1}{2}})}{\sqrt{14}}]Subtract the exponents since you are dividing
*[Tex \LARGE \frac{\sqrt{42}(a^{\frac{1}{2}})(b^{2})}{\sqrt{14}}]
*[Tex \LARGE \sqrt{\frac{42}{14}}(a^{\frac{1}{2}})(b^{2})]Divide the square roots as one (in other words *[Tex \LARGE \frac{\sqrt{x}}{\sqrt{y}}=\sqrt{\frac{x}{y}}]

*[Tex \LARGE \sqrt{3}(a^{\frac{1}{2}})(b^{2})]Rewrite the fractional exponent as a radical
*[Tex \LARGE \sqrt{3}\sqrt{a}b^{2}]There's your simplified answer