Question

Which expression is equivalent to ^5√32x^5y^10z^15

Answer 1

$\sqrt[5]{32x^5y^{10}z^{15}}=\sqrt[5]{32}\cdot\sqrt[5]{x^5}\cdot\sqrt[5]{(y^2)^5}\cdot\sqrt[5]{(z^3)^5}=2xy^2z^3$

Used:

$(a^n)^m=a^{n\cdot m}\\\\\sqrt[n]{a^n}=a$

Answer: b- 2xy^2z^3

Answer 2

Answer:  Option 'b' is correct.

Step-by-step explanation:

Since we have given that

$^5\sqrt{32x^5y^{10}z^{15}}$

We need to find the expression which would be equivalent to the above expression.

As we know that

32=2⁵

So, it becomes,

$^5\sqrt{2^5x^5y^{10}z^{15}}\\\\=(2^5)^{\frac{1}{5}}\times (x^5)^{\frac{1}{5}}\times (y^{10}){\frac{1}{5}}\times (z^{15})^{\frac{1}{5}}\\\\=2\times x\times y^2\times z^3\\\\=2xy^2z^3$

Hence, Option 'b' is correct.