Question

Which expression is equivalent to (x Superscript one-fourth Baseline y Superscript 16 Baseline) Superscript one-half?

Answer 1

Answer:

$x^{\frac{1}{8}}y^8$.

Step-by-step explanation:

The given expression is

$(x^{\frac{1}{4}}y^{16})^{\frac{1}{2}}$

We need to find the expression, which is equivalent to the given expression.

The given expression can be rewritten as

$(x^{\frac{1}{4}})^{\frac{1}{2}}(y^{16})^{\frac{1}{2}}$     $[\because (ab)^m=a^mb^m]$

$(x^{\frac{1}{4}\times \frac{1}{2}})(y^{16\times \frac{1}{2}})$     $[\because (a^m)^n=a^{mn}]$

$x^{\frac{1}{8}}y^8$

Therefore, the required expression is $x^{\frac{1}{8}}y^8$.

Answer 2

The simplified form of the indices is $x^{1/4}y^8$

Given the expression:

$(x^{1/4}y^{16})^{1/2}$

Using the law of indices below:

$(a^m)^n = a^{mn}$

 

Multiplying the power will give:

$= (x^{1/4})^{1/2} \cdot (y^{16})^{1/2}\\=x^{1/4}y^8$

 

Hence the simplified form of the indices is $x^{1/4}y^8$

Learn more on indices here: brainly.com/question/8952483