Question

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

a- 2y^5z^10
b- 2xy^2z^3
c- 6y^5z^10
d- 6xy^2z^3

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.

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)^{(1)/(5)}* (x^5)^{(1)/(5)}* (y^(10)){(1)/(5)}* (z^(15))^{(1)/(5)}\\\\=2* x* y^2* z^3\\\\=2xy^2z^3`

Hence, Option 'b' is correct.