the fourth root of 121x^5y^-6

Question

 I need to be able to simplify this problem completely while also showing a step by step process.

Answer 1

Mark has the right approach.  However, we want to put the full answer in radical form.  In addition to this, he also missed the negative 6 as the exponent of y.   So we will have

 

√(11) * ⁴√(x⁵) * √(1 / y³)

 

√(11) * ⁴√(x⁵) * √(1) / √(y³)

 

Note:   ⁴√ means the 4th root.

 

 

Breaking each radical by their factors, we obtain

 

[√(11) * ⁴√(x⁴) * ⁴√(x)] / [√(y²) * √(y)]

 

 

Using the rule     ⁿ√(xⁿ) = x     to simplify

 

[√(11) * x * ⁴√(x)] / [y * √(y)]

 

 

Multiply like radicals.

 

(x / y) * √(11 / y) * ⁴√(x)

 

 

 

Answer 2

[121x⁵y⁶]^1/4  The fourth root of something is that something to the 1/4 power.

= (121)^1/4(x⁵)^1/4(y⁶)^1/4

= (11²)^1/4x^5/4y^3/2  Recall that (x^a)^b = x^ab

= (11)^1/2x^5/4y^3/2

= √11 x^5/4y^3/2