the tripled product of 6a and b^2. I got 216a^3b^6, but my teacher says that this is wrong. my equation is \(6ab^2)^3 is this wrong?
It says the tripled product so the equation will be:
3(6a*b^2)
And if you simplify that:
3(6ab^2)
=18ab^2
the tripled product of 6a and b^2.
To solve this problem, suppose we have the expression \(6a \cdot b^2\), and we want to find its tripled product.
Triple the product means multiplying the expression by 3. So, we have \(3 \cdot (6a \cdot b^2)\).
To get the answer, we multiply the coefficient (3) with each term in the expression:
\(3 \cdot 6a \cdot b^2 = 18ab^2\).
Hence, the tripled product of \(6a \cdot b^2\) is \(18ab^2\).
It seems that you raised the entire expression to the power of 3, which is why you got the incorrect answer of \(216a^3b^6\). Instead, apply the power of 3 only to the coefficient, not the variables.
(6ab^2)^3 = 216a^3b^6
You are correct. Better see where your teacher went astray...