Question

simplify. express your answer using positive exponents.
$6f^5g \cdot 3f^7g$

Explanation:

Step1: Multiply the coefficients

Multiply 6 and 3.
$6\times3 = 18$

Step2: Multiply the \( f \)-terms using exponent rule \( a^m \cdot a^n = a^{m + n} \)

For \( f^5 \cdot f^7 \), add the exponents: \( 5 + 7 = 12 \), so \( f^5 \cdot f^7 = f^{12} \)

Step3: Multiply the \( g \)-terms using exponent rule \( a^m \cdot a^n = a^{m + n} \)

For \( g \cdot g \), add the exponents (note \( g = g^1 \)): \( 1 + 1 = 2 \), so \( g \cdot g = g^2 \)

Step4: Combine the results

Multiply the coefficient, \( f \)-term, and \( g \)-term together.
$18\times f^{12}\times g^2 = 18f^{12}g^2$

Answer:

$18f^{12}g^2$