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Simplify. Express your answer using positive exponents.

(2ab^(7))(6a^(9)b)

Simplify. Express your answer using positive exponents. $\newline$ $\left(2 a b^{7}\right)\left(6 a^{9} b\right)$

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Multiply and divide powers: variable bases

Full solution

Q. Simplify. Express your answer using positive exponents.

\newline

\left(2 a b^{7}\right)\left(6 a^{9} b\right)

Multiply Coefficients: Multiply the coefficients (numerical parts) of the two terms. $\newline$ We have $2$ and $6$ as coefficients, so we multiply them together. $\newline$ $2 \times 6 = 12$
Add Exponents for 'a': Multiply the variables with the same base by adding their exponents. $\newline$ For the variable 'a', we have $a^1$ (implied) in the first term and $a^9$ in the second term. $\newline$ $a^1 \times a^9 = a^{(1+9)} = a^{10}$
Add Exponents for 'b': Multiply the variables with the same base 'b' by adding their exponents. $\newline$ For the variable 'b', we have $b^7$ in the first term and $b^1$ (implied) in the second term. $\newline$ $b^7 \times b^1 = b^{(7+1)} = b^8$
Combine Results: Combine the results from Step $1$ , Step $2$ , and Step $3$ to write the final expression. $\newline$ We have the coefficient $12$ , $a^{10}$ , and $b^8$ . $\newline$ So, the final expression is $12a^{10}b^8$ .

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