Question

Which expression is equivalent to 3 cube root (343x^9 y^12 z^6) ? 7x3y4z2 7x3y6z2 49x3y6z2 49x3y4z2

Answer 1

cube root of 343 = 7

of x^9 it is x^3 ( because x^9 = x^3 * x^3 * x^3)

of y^12 it is y^4

of z^6 it is z^2

So the correct choice is A

Answer 2

A.
`7x^3*y^4*z^2`

Explanation:

We have been given an expression
`\sqrt[3]{343x^9y^(12)z^6}`. We are asked to find the equivalent expression to our given expression.

Using exponent property
`(a^b)^c=a^(b\cdot c)` we can rewrite the terms of our given expression as:

`\sqrt[3]{7^3*(x^3)^3*(y^4)^(3)*(z^2)^3}`

Using property
`\sqrt[n]{a^n}=a` we will get,

`7x^3*y^4*z^2`

Therefore, the simplified form of our given expression would be
`7x^3*y^4*z^2` and option A is the correct choice.