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Simplify. Express your answer using positive exponents.
7u^(9)*2u^(2)*7u

Simplify. Express your answer using positive exponents. $\newline$ $7 u^{9} \cdot 2 u^{2} \cdot 7 u$

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Simplify exponential expressions using the multiplication and division rules

Full solution

Q. Simplify. Express your answer using positive exponents.

\newline

7 u^{9} \cdot 2 u^{2} \cdot 7 u

Group Terms with Same Base: Group the coefficients and powers that have the same base. $\newline$ We have the expression $7u^{9}\cdot2u^{2}\cdot7u$ . We can group the coefficients ( $7$ , $2$ , and $7$ ) and the powers of $u$ ( $u^{9}$ , $u^{2}$ , and $u$ ) together. $\newline$ $7u^{9}\cdot2u^{2}\cdot7u = (7 \cdot 2 \cdot 7) \cdot (u^{9} \cdot u^{2} \cdot u)$
Multiply Coefficients: Multiply the coefficients. $\newline$ Now we multiply the coefficients $7$ , $2$ , and $7$ together. $\newline$ $7 \times 2 \times 7 = 14 \times 7 = 98$
Combine Exponents: Combine the powers of $u$ using the property of exponents. $\newline$ When multiplying powers with the same base, we add the exponents. $\newline$ $u^{9} \times u^{2} \times u = u^{9 + 2 + 1} = u^{12}$
Write in Simplest Form: Write the expression in simplest form. $\newline$ Now we combine the results from Step $2$ and Step $3$ to write the expression in simplest form. $\newline$ $7u^{9}$ $2u^{2}$ $7u = 98 \times u^{12} = 98u^{12}$

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