[tex] \sqrt[5]{32x^5y^{10}z^{15}}=\sqrt[5]{32}\cdot\sqrt[5]{x^5}\cdot\sqrt[5]{(y^2)^5}\cdot\sqrt[5]{(z^3)^5}=2xy^2z^3 [/tex]
Used:
[tex](a^n)^m=a^{n\cdot m}\\\\\sqrt[n]{a^n}=a[/tex]
Answer: b- 2xy^2z^3
Answer: Option 'b' is correct.
Step-by-step explanation:
Since we have given that
[tex]^5\sqrt{32x^5y^{10}z^{15}}[/tex]
We need to find the expression which would be equivalent to the above expression.
As we know that
32=2⁵
So, it becomes,
[tex]^5\sqrt{2^5x^5y^{10}z^{15}}\\\\=(2^5)^{\frac{1}{5}}\times (x^5)^{\frac{1}{5}}\times (y^{10}){\frac{1}{5}}\times (z^{15})^{\frac{1}{5}}\\\\=2\times x\times y^2\times z^3\\\\=2xy^2z^3[/tex]
Hence, Option 'b' is correct.
