Question

Need answer please!!!!

Answer 1

For this case we must simplify the following expression:

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

By definition of properties of powers and roots, we have to:

$\sqrt [n] {a ^ m} = a ^ {\frac {m} {n}}$

Then, rewriting the expression:

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

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

By definition of properties of division of powers of equal base we have to;

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

Rewriting the expression:

$\frac{c*d^{3-(-2)}}{2c*\sqrt{c}}\\\frac{c*d^5}{2c*\sqrt{c}}\\\frac{d^5}{2\sqrt{c}}$

Answer:

Option B

Answer 2

Answer:

B

Step-by-step explanation:

Using the rules of radicals/ exponents

• $\frac{\sqrt{a} }{\sqrt{b} }$ ⇔ $\sqrt{\frac{a}{b} }$, hence

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

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

= $\frac{d^5}{2\sqrt{c} }$ → B