Answer:
[tex]2^{\frac{18}{11}}[/tex]
Step-by-step explanation:
The given expression is
[tex]\sqrt[11]{y^2z^4}[/tex]
The exponent property [tex]\sqrt[n]{x^ay^b}=x^{a/n}y^{b/n}[/tex]
Applying this exponent property, we have
[tex]\sqrt[11]{y^2z^4}\\\\=y^{2/11}z^{4/11}[/tex]
Now, the given numeric values are x = 9, y= 8, and z= 16
On substituting these values in the simplified expression, we get
[tex](2)^{2/11}(16)^{4/11}[/tex]
This can be further simplified by writing [tex]16=2^4[/tex]
[tex](2)^{2/11}(2^4)^{4/11}\\\\(2)^{2/11}(2)^{16/11}[/tex]
Now, applying the product rule of exponent: [tex]x^a\cdot x^b=x^{a+b}[/tex]
[tex](2)^{2/11+16/11}\\\\=2^{\frac{18}{11}}[/tex]
