Question

simplify. express your answer using positive exponents.
(8fg⁶h)(8f³g⁹h)

Explanation:

Step1: Multiply the coefficients

Multiply the coefficients 8 and 8. So, \( 8\times8 = 64 \).

Step2: Multiply the \( f \)-terms

Use the rule \( a^m \times a^n = a^{m + n} \) for the \( f \)-terms. Here, \( f^1\times f^3 = f^{1 + 3}=f^4 \).

Step3: Multiply the \( g \)-terms

Apply the same exponent rule for \( g \)-terms: \( g^6\times g^9 = g^{6 + 9}=g^{15} \).

Step4: Multiply the \( h \)-terms

For \( h \)-terms: \( h^1\times h^1 = h^{1 + 1}=h^2 \).

Step5: Combine all terms

Combine the results from steps 1 - 4: \( 64f^4g^{15}h^2 \).

Answer:

\( 64f^4g^{15}h^2 \)