Question

Perform the indicated operations. Write the answer using only positive exponents. Assume all variables represent positive real numbers.
${\left(\frac{b^{-5/6}}{n^{-7/4}}\right)}^2{\left(\frac{n^{1/3}}{b^{1/7}}\right)}^{-3}$

• A. $\frac{b^{44/21}}{n^{9/2}}$
• B. $\frac{n^{5/2}}{b^{26/21}}$
• C. $\frac{n^{9/2}}{b^{44/21}}$
• D. $\frac{b^{26/21}}{n^{5/2}}$

Answer 1

The correct option is B $\frac{n^{5/2}}{b^{26/21}}$

Given,

${\left(\frac{b^{-\frac{5}{6}}}{n^{-\frac{7}{4}}}\right)}^2{\left(\frac{n^{\frac{1}{3}}}{b^{\frac{1}{7}}}\right)}^{-3}$

$={\left(\frac{b^{-\frac{5}{6}}}{n^{-\frac{7}{4}}}\right)}^2\frac{1}{{\left(\frac{n^{\frac{1}{3}}}{b^{\frac{1}{7}}}\right)}^3}$

$=\frac{n^{\frac{7}{2}}}{b^{\frac{5}{3}}}\cdot \frac{1}{{\left(\frac{n^{\frac{1}{3}}}{b^{\frac{1}{7}}}\right)}^3}$

$=\frac{n^{\frac{7}{2}}}{b^{\frac{5}{3}}}\cdot \frac{b^{\frac{3}{7}}}{n}$

$=\frac{n^{\frac{7}{2}}{b}^{\frac{3}{7}}}{b^{\frac{5}{3}}n}$

$=\frac{n^{\frac{7}{2}-1}}{b^{\frac{5}{3}-\frac{3}{7}}}$

$=\frac{n^{\frac{5}{2}}}{b^{\frac{26}{21}}}$