Question

27. Which expression is equivalent to

Answer 1

You need to use these two rules of exponents:
To raise a product to a power, raise each factor to the power.
To raise a power to a power, multiply the powers.

The product inside the parentheses is being raised to the power 1/2.
Raise each factor to the power 1/2.


`\left( x^{ (1)/(4) } y^(16) \right) ^{(1)/(2)} =`


`= \left( x^{ (1)/(4) } \right)^{(1)/(2)} \left( y^(16) \right) ^{(1)/(2)}`

Now multiply the exponents.


`= x^{ (1)/(8) } y^(8)`

Finally, use the definition of a rational exponent to change the exponent of x into a root.


`= (\sqrt[8]{x}) y^(8)`

Answer 2

I Had To Answer It On A Notepad. Hope This Helps.