Answer:
The equivalent expression is [tex]\Rightarrow \dfrac{4x^4}{y^6}[/tex]
Step-by-step explanation:
Given: [tex](16x^8y^{-12})^{1/2}[/tex]
We need to simplify the expression. We will distribute radical with each term inside the parentheses.
[tex]\Rightarrow (16x^8y^{-12})^{1/2}[/tex]
Distribute the radical
[tex]\Rightarrow 16^{1/2}\cdot x^{8\cdot 1/2\cdot y^{-12\cdot 1/2}[/tex]
[tex]\Rightarrow 4\cdot x^4\cdot y^{-6}[/tex]
[tex]\Rightarrow 4x^4y^{-6}[/tex]
Now we will simplify the negative exponent.
[tex]\Rightarrow \dfrac{4x^4}{y^6}[/tex]
Hence, The equivalent expression is [tex]\Rightarrow \dfrac{4x^4}{y^6}[/tex]
