Question

21....................

Answer 1

Answer:

The answer is (b) ⇒$\frac{d^{5} }{2\sqrt{c} }$

Step-by-step explanation:

∵ $\frac{\sqrt{c^{2}d^{6}}}{\sqrt{4c^{3}d^{-4}}}$

∵ √x² = x ⇒ that means to cancel the square root divide

  the power by 2

∴ $\sqrt{c^{2}d^{6}}=cd^{3}$

∵ √4 = 2 ⇒ √2×2 = √2² = 2

∵ √c³  = $c^{\frac{3}{2}}$

∴ $\sqrt{4c^{3}d^{-4}}=2c^{\frac{3}{2}}d^{-2}$

∴ $\frac{cd^{3}}{2c^{\frac{3}{2}}d^{-2}}$

∵ In the same base with multiplication we add the power,

  in same base with division we subtract the power

∴ $\frac{1}{2}c^{1-\frac{3}{2}}d^{3-(-2)}=\frac{1}{2}c^{\frac{-1}{2}}d^{5}=$

  $\frac{d^{5}}{2c^{\frac{1}{2}}}=\frac{d^{5}}{2\sqrt{c}}$ ⇒  $c^{\frac{1}{2}}=\sqrt{c}$

∴ The answer is (b) ⇒ $\frac{d^{5}}{2\sqrt{c}}$

Answer 2

Answer:

b. $\frac{d^{5}}{2\sqrt{c} }$

Step-by-step explanation:

The given expression is

$\frac{\sqrt{c^2d^6} }{\sqrt{4c^3d^{-4}} }$

We simplify the radicand using the property;  $\frac{a^m}{a^n} =a^{m-n}$

$\frac{\sqrt{d^{6--4}} }{\sqrt{4c^{3-2}} }$

$\frac{\sqrt{d^{10}} }{\sqrt{4c^{1}} }$

$\frac{d^{5}}{2\sqrt{c} }$