Question

homework 6.2 multiplication of monomials simplify each expression. 5. \\((2ab^2f^2)(4a^3b^2f^2)\\) type a response

Explanation:

Step1: Multiply the coefficients

Multiply the numerical coefficients \(2\) and \(4\).
\(2\times4 = 8\)

Step2: Multiply the \(a\)-terms

Use the rule of exponents \(a^m\times a^n=a^{m + n}\) for \(a^1\) and \(a^3\).
\(a^1\times a^3=a^{1 + 3}=a^4\)

Step3: Multiply the \(b\)-terms

Use the rule of exponents for \(b^2\) and \(b^2\).
\(b^2\times b^2=b^{2+2}=b^4\)

Step4: Multiply the \(f\)-terms

Use the rule of exponents for \(f^2\) and \(f^2\).
\(f^2\times f^2=f^{2 + 2}=f^4\)

Step5: Combine all the terms

Multiply the results from Step 1, Step 2, Step 3 and Step 4 together.
\(8\times a^4\times b^4\times f^4 = 8a^4b^4f^4\)

Answer:

\(8a^4b^4f^4\)