Question

Write the equivalent expression to

Answer 1

Answer:

Step-by-step explanation:

Begin by changing the radical form to exponential form:

$((1024w^{-2}x^{-3}y^6z^{-1)^2)^{\frac{1}{5} }$  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:

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

$1024^{\frac{2}{5}}w^{-\frac{4}{5}}x^{-\frac{6}{5}}y^{\frac{12}{5}}z^{-\frac{2}{5}$

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:

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