Question

Solve:
$\frac{5^{\frac{1}{3}}\times 5^2\times 5^{\frac{-1}{2}}}{5^{\frac{4}{5}}÷\sqrt{5}÷5^{\frac{2}{5}}}\times \frac{5^{\frac{4}{3}}}{5^{\frac{1}{10}}}$

• A. $5^{\frac{11}{3}}$
• B. $5^{\frac{10}{3}}$
• C. $5^{-\frac{10}{3}}$
• D. $5^{\frac{12}{3}}$

Answer 1

The correct option is A $5^{\frac{11}{3}}$

Here, we need to solve first fraction and multiply with second fraction.
Solving we get:
$\frac{5^{\frac{1}{3}}\times 5^2\times 5^{\frac{-1}{2}}}{5^{\frac{4}{5}}÷\sqrt{5}÷5^{\frac{2}{5}}}=\frac{5^{(\frac{1}{3}+2)}\times 5^{\frac{-1}{2}}}{5^{\frac{4}{5}}÷5^{\frac{1}{2}}÷5^{\frac{2}{5}}}(\because a^m\times a^n=a^{m+n})=\frac{5^{\left(\frac{7}{3}\right)}\times 5^{\frac{-1}{2}}}{5^{(\frac{4}{5}}{}^{-\frac{1}{2})}÷5^{\frac{2}{5}}}(\because a^m÷a^n=a^{m-n})\frac{5^{(\frac{7}{3}-\frac{1}{2})}}{5^{\frac{3}{10}}÷5^{\frac{2}{5}}}=\frac{5^{\frac{7}{3}}}{5^{\frac{3}{10}}÷5^{\frac{2}{5}}}=\frac{5^{\frac{7}{3}}}{5^{\frac{-1}{10}}}$Now, multiplying with second term we get:
$\frac{5^{\frac{7}{3}}}{5^{\frac{-1}{10}}}\times \frac{5^{\frac{4}{3}}}{5^{\frac{1}{10}}}$$\frac{5^{(\frac{7}{3}+\frac{4}{3})}}{5^{(\frac{-1}{10}+\frac{1}{10})}}=\frac{5^{\frac{11}{3}}}{5^0}=5^{\frac{11}{3}}$