High School

Which expression is equivalent to [tex]3\sqrt[3]{343x^9 y^{12} z^6}[/tex]?

A. [tex]7x^3 y^4 z^2[/tex]
B. [tex]7x^3 y^6 z^2[/tex]
C. [tex]49x^3 y^6 z^2[/tex]
D. [tex]49x^3 y^4 z^2[/tex]

Answer :

Answer:

A. [tex]7x^3*y^4*z^2[/tex]

Step-by-step explanation:

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

Using exponent property [tex](a^b)^c=a^{b\cdot c}[/tex] we can rewrite the terms of our given expression as:

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

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

[tex]7x^3*y^4*z^2[/tex]

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

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