Question

Simplify Fully (Negative powers)

Answer 1

`(y^2)/(4x^5)`

Explanation:

Used Exponents Properties :

`\blacksquare \left( a* b\right)^(n) =a^(n)* b^(n)\\\blacksquare \left( a^(n)\right)^(m) =a^(n* m)\\\blacksquare \left( (a)/(b) \right)^(n) =(a^(n))/(b^(n))`

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`\begin{aligned}\left((256 * x^(20))/(y^8)\right)^{-(1)/(4)} & =\left((y^8)/(2^8 * x^(20))\right)^{(1)/(4)} \\& =\frac{\left(y^8\right)^{(1)/(4)}}{\left(2^8 * x^(20)\right)^{(1)/(4)}} \\& =\frac{y^{8 * (1)/(4)}}{\left(2^8\right)^{(1)/(4)} *\left(x^(20)\right)^{(1)/(4)}} \\& =\frac{y^{(8)/(4)}}{2^{(8)/(4)} * x^{(20)/(4)}} \\& =(y^2)/(2^2 x^5)\\& =(y^2)/(4 x^5)\end{aligned}`