Respuesta :
To solve the problem we must know the Basic Rules of Exponentiation.
Basic Rules of Exponentiation
- [tex]x^ax^b = x^{(a+b)}[/tex]
- [tex]\dfrac{x^a}{x^b} = x^{(a-b)}[/tex]
- [tex](a^a)^b =x^{(a\times b)}[/tex]
- [tex](xy)^a = x^ay^a[/tex]
- [tex]x^{\frac{3}{4}} = \sqrt[4]{x^3}= (\sqrt[3]{x})^4[/tex]
The solution of the expression is [tex]\dfrac{4x^4}{y^6}[/tex].
Explanation
Given to us
- [tex](16x^8y^{12})^{\frac{1}{2}}[/tex]
Solution
We know that 16 can be reduced to [tex]2^4[/tex],
[tex]=(2^4x^8y^{12})^{\frac{1}{2}}[/tex]
Using identity [tex](xy)^a = x^ay^a[/tex],
[tex]=(2^4)^{\frac{1}{2}}(x^8)^{\frac{1}{2}}(y^{12})^{\frac{1}{2}}[/tex]
Using identity [tex](a^a)^b =x^{(a\times b)}[/tex],
[tex]=(2^{4\times \frac{1}{2}})\ (x^{8\times\frac{1}{2}})\ (y^{12\times{\frac{1}{2}}})[/tex]
Solving further
[tex]=2^2x^4y^{-6}[/tex]
Using identity [tex]\dfrac{x^a}{x^b} = x^{(a-b)}[/tex],
[tex]=\dfrac{2^2x^4}{y^6}[/tex]
[tex]=\dfrac{4x^4}{y^6}[/tex]
Hence, the solution of the expression is [tex]\dfrac{4x^4}{y^6}[/tex].
Learn more about Exponentiation:
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