Question

Solve ab^-1c^3/5 divided by a^-3/2b^2c^1/3xab^2c^2

Answer 1

Question:

$\frac{ {ab}^{ - 1} \times - 1 {c}^{ \frac{3}{5} } }{ \frac{ {a}^{ - 3} }{2 {b}^{2} } \times 2 {c}^{ \frac{1}{3} } \times ab \times {c}^{2} }$

Answer:

$\underline\bold{ {-c}^{\frac{18}{5}}{4b}^{-2} } \: is \: the \: answer.$

Step-by-step explanation:

$\frac{ {ab}^{ - 1} \times - 1 {c}^{ \frac{3}{5} } }{ \frac{ {a}^{ - 3} }{2 {b}^{2} } \times 2 {c}^{ \frac{1}{3} } \times ab \times {c}^{2} }$

Now rationalising the numerator,

$\Rightarrow {ab}^{ - 1} \times - 1 {c}^{ \frac{3}{5} }$

${ab}^{ - 1} = \frac{1}{ab} = \frac{1}{a} \times \frac{1}{b}$

$\Rightarrow \frac{1}{a} \times \frac{1}{b} \times - {c}^{ \frac{3}{5} }$

Now rationalising the denominator,

$\frac{ {a}^{ - 3} }{2 {b}^{2} } \times 2 {c}^{ \frac{1}{3} } \times a{b}^{2} \times {c}^{2}$

$= \frac{2 {b}^{2} }{ {a}^{3} } \times 2 {c}^{ \frac{1}{3} }$

$= \frac{4 {b}^{2} \times 2 {c}^{ \frac{1}{3} } }{ {a}^{3} }$

Now,

$\Rightarrow \frac{ \frac{1}{a} \times \frac{1}{b} \times - {c}^{ \frac{3}{5} } }{ \frac{4 {b}^{2} \times {c}^{ \frac{2}{3} } }{ {a}^{3} }×ab×{c}^{2} }$

$\Rightarrow \frac{ - {c}^{ \frac{3}{5} } }{4b {c}^{ \frac{1}{3} } × {c}^{2} }$

$\Rightarrow \frac{ - {c}^{ \frac{3}{5} } \times {c}^{ \frac{3}{1} }×{c}^{2} }{{4b}^{2}}$

$\Rightarrow \frac{ - {c}^{ \frac{18}{5} } }{{4b}^{2}}$

$\Rightarrow\boxed{{-c}^{\frac{18}{5}}{4b}^{-2}}$

Formula used:

${mn}^{ - 1} = \frac{1}{mn}$

$\frac{ {m}^{a} }{ {n}^{b} } = {m}^{a} {n}^{ - b}$