what expression raised to the third power is
81x^12y^8z^16
answer is 3x^4y^2z^4
No. 3 cubed is 27, and 4 cubed is 64, and (z^4)^3= z^12
To find an expression raised to the third power that is equal to 81x^12y^8z^16, you need to take the cube root of each term in the expression.
Let's break down each term:
- For 81, the cube root is 3 because 3*3*3 = 27.
- For x^12, the cube root is x^4 because (x^4)*(x^4)*(x^4) = x^12.
- For y^8, the cube root is y^2 because (y^2)*(y^2)*(y^2) = y^8.
- For z^16, the cube root is z^4 because (z^4)*(z^4)*(z^4) = z^16.
Putting it all together, the expression raised to the third power that is equal to 81x^12y^8z^16 is 3x^4y^2z^4.