Respuesta :
Answer:
Equivalent expression is [tex]x^{\frac{1}{8}}y^{8}[/tex]
Step-by-step explanation:
Given Expression is
[tex](x^{\frac{1}{4}}y^{16})^{\frac{1}{2}}[/tex]
We have to find Equivalent expression to given expression.
using law of exponent , [tex](ab)^x=a^xb^x[/tex]
we get,
[tex]\implies(x^{\frac{1}{4}})^{\frac{1}{2}}(y^{16})^{\frac{1}{2}}[/tex]
now using another law of exponent, [tex](x^a)^b=x^{ab}[/tex]
we get,
[tex]\implies x^{\frac{1}{4}\times\frac{1}{2}}y^{16\times\frac{1}{2}}[/tex]
[tex]\implies x^{\frac{1}{8}}y^{8}[/tex]
Therefore, Equivalent expression is [tex]x^{\frac{1}{8}}y^{8}[/tex]
Answer:
[tex]x^{\frac{1}{8}}y^{8}[/tex]
Step-by-step explanation:
Consider the given expression
[tex](x^{\frac{1}{4}}y^{16})^{\frac{1}{2}}[/tex]
According to the distributive property of exponent,
[tex](ab)^m=a^mb^m[/tex]
Using distributive property of exponent we get
[tex](x^{\frac{1}{4}})^{\frac{1}{2}}(y^{16})^{\frac{1}{2}}[/tex]
Using the property of exponent we get
[tex]x^{\frac{1}{4}\times \frac{1}{2}}y^{16\times \frac{1}{2}}[/tex] [tex][\because (a^m)^n=a^{mn}][/tex]
[tex]x^{\frac{1}{8}}y^{8}[/tex]
Therefore, the expression [tex]x^{\frac{1}{8}}y^{8}[/tex] is equivalent to the given expression.
