Question

Write the equivalent expression to

Answer 1

Explanation:

Begin by changing the radical form to exponential form:

`((1024w^(-2)x^(-3)y^6z^{-1)^2)^{(1)/(5) }` There are a couple of ways to do this, but let's distribute the power of 2 into the parenthesis first by using the power to power rule of multiplication:

`(1024^2w^(-4)x^(-6)y^(12)z^(-2))^{(1)/(5)` Now we can use the same rule of power to power and distribute the power of 1/5 in:

`1024^{(2)/(5)}w^{-(4)/(5)}x^{-(6)/(5)}y^{(12)/(5)}z^{-(2)/(5)`

The first term simplifies down to 16, and then in order to make the negative exponents positive, we move them to the denominator of a fraction, leaving the positive one where it is:

`\frac{16y^{(12)/(5)} }{w^{(4)/(5)}x^{(6)/(5) }z^{(2)/(5) } }` which is the third choice down