Simplify. Express your answer using positive exponents.

Question

(3fg^3h^6)(4fg^5h^4)

Answer 1

To simplify the expression \((3fg^3h^6)(4fg^5h^4)\), we start by multiplying the coefficients and combining the like terms.

1. Multiply the coefficients: \[ 3 \times 4 = 12 \]

2. Combine the \(f\) terms: \[ f^1 \times f^1 = f^{1+1} = f^2 \]

3. Combine the \(g\) terms: \[ g^3 \times g^5 = g^{3+5} = g^8 \]

4. Combine the \(h\) terms: \[ h^6 \times h^4 = h^{6+4} = h^{10} \]

Now, we can put it all together: \[ (3fg^3h^6)(4fg^5h^4) = 12f^2g^8h^{10} \]

Thus, the simplified expression is: \[ \boxed{12f^2g^8h^{10}} \]