Question

answer the question please​

Answer 1

Question

$\sf\large \dfrac{ {x}^{ \frac{7}{2} } \times \sqrt{y} }{ {x}^{ \frac{5}{2} } \times \sqrt{ {y}^{3} } }$

$\sf\huge\bold{\underline{\underline{{Solution}}}}$

$\sf\large \boxed{ \bold{\star\:\sqrt{a} = {a}^{ \frac{1}{2} }} \:\star}$

$\sf \longmapsto\large \dfrac{ {x}^{ \frac{7}{2} } \times {y}^{ \frac{1}{2} } }{ {x}^{ \frac{5}{2} } \times { {(y}^{3} )}^{ \frac{1}{2} } }$

$\sf \longmapsto\large \dfrac{ {x}^{ \frac{7}{2} } \times {y}^{ \frac{1}{2} } }{ {x}^{ \frac{5}{2} } \times {y}^{ \frac{3}{2} } }$

Concepts

If bases are same with different powers then their powers gets added in multiplication and gets substracted while we divide.

$\sf \large\boxed{ \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}}$

$\sf\large \boxed{ {a}^{m} \times {a}^{n} = {a}^{m + n}}$

$\sf \longmapsto\large {x}^{ \frac{7}{2} - \frac{5}{2} } \times {y}^{ \frac{1}{2} - \frac{3}{2} }$

$\sf \longmapsto \large{x}^{ \frac{2}{2} } \times {y}^{ \frac{ - 2}{2} }$

$\sf \longmapsto \: x \times {y}^{ - 1}$

$\sf= \large \bold{ \dfrac{x}{y} }$

Answer 2

Answer:

the picture shows the answer for your question

We can write

$x {7 \div 2 = x5\div 2 \: \times x}$

as well as

${y3 \div 2 =y1 \div 2 \times y {}^{} }^{}$