Simplify the radical expression. (Multiple Choice)

Question

 

a. |c⁴⁰|d²⁵

b. c⁴⁰d²⁵

c. cd²⁵

d. c⁴⁰|d²⁵|

Answer 1

Taking the square root is the same as raising to the power of 1/2.  So this expression is the same as:

 

(c⁸⁰d⁵⁰)^1/2

 

Now use the product rule for powers:  (xy)^a = x^a y^a

 

In this case it means:

 

(c⁸⁰d⁵⁰)^1/2

= (c⁸⁰)^1/2  (d⁵⁰)^1/2

 

Now use the power rule for powers.  (x^a)^b = x^ab.  So:

 

(c⁸⁰)^1/2 = c^{(80 * 1/2)} = c⁴⁰

(d⁵⁰)^1/2 = d^{(40 * 1/2)} = d²⁵

 

So (c⁸⁰)^1/2  (d⁵⁰)^1/2 = c⁴⁰ d²⁵

 

Therefore the answer is b