Answer :

Answer:

B

Step-by-step explanation:

Using the rules of radicals/ exponents

• [tex]\frac{\sqrt{a} }{\sqrt{b} }[/tex] ⇔ [tex]\sqrt{\frac{a}{b} }[/tex], hence

[tex]\sqrt{\frac{c^2d^6}{4c^3d^-4} }[/tex] ← simplify

= [tex]\sqrt{\frac{1}{4}(\frac{1}{c})(d^(10))  }[/tex]

= [tex]\frac{d^5}{2\sqrt{c} }[/tex] → B

carlosego

For this case we must simplify the following expression:

[tex]\frac {\sqrt {c ^ 2 * d ^ 6}} {\sqrt {4c ^ 3 * d ^ {- 4}}}[/tex]

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

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

Then, rewriting the expression:

[tex]\frac {c ^ {\frac {2} {2}} * d {\frac {6} {2}}} {2 * c ^ {\frac {2} {2}} * d ^ {\frac { -4} {2}} * \sqrt {c}}[/tex]

[tex]\frac{c*d^3}{2c*d^{-2}*\sqrt{c}}[/tex]

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

[tex]\frac {a ^ m} {a ^ n} = a ^ {m-n}[/tex]

Rewriting the expression:

[tex]\frac{c*d^{3-(-2)}}{2c*\sqrt{c}}\\\frac{c*d^5}{2c*\sqrt{c}}\\\frac{d^5}{2\sqrt{c}}[/tex]

Answer:

Option B

Other Questions