Question

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

Answer 1

b.
`(d^(5))/(2√(c) )`

Explanation:

The given expression is

`\frac{√(c^2d^6) }{\sqrt{4c^3d^(-4)} }`

We simplify the radicand using the property;
`(a^m)/(a^n) =a^(m-n)`

`\frac{\sqrt{d^(6--4)} }{\sqrt{4c^(3-2)} }`

`\frac{\sqrt{d^(10)} }{\sqrt{4c^(1)} }`

`(d^(5))/(2√(c) )`

Answer 2

The answer is (b) ⇒
`(d^(5) )/(2√(c) )`

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^{(3)/(2)}`

∴
`\sqrt{4c^(3)d^(-4)}=2c^{(3)/(2)}d^(-2)`

∴
`\frac{cd^(3)}{2c^{(3)/(2)}d^(-2)}`

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

in same base with division we subtract the power

∴
`(1)/(2)c^{1-(3)/(2)}d^(3-(-2))=(1)/(2)c^{(-1)/(2)}d^(5)=`

`\frac{d^(5)}{2c^{(1)/(2)}}=(d^(5))/(2√(c))` ⇒
`c^{(1)/(2)}=√(c)`

∴ The answer is (b) ⇒
`(d^(5))/(2√(c))`