Simplify. Express your answer using positive exponents. (10f^6 * 8f)/2f^9 ______

Multiply and Combine Terms: Multiply the coefficients (numbers) and combine the f terms using the product rule for exponents. The product rule states that when you multiply two powers with the same base, you add the exponents. 10f^6 * 8f = 80f^(6+1) = 80f^7Divide by 2f^9: Divide the new expression by 2f^9 using the quotient rule for exponents. The quotient rule states that when you divide two powers with the same base, you subtract the exponents. (80f^7)/2f^9 = (80/2)f^(7-9) = 40f^(-2)Express with Positive Exponents: Express the answer using positive exponents. To express f^(-2) with a positive exponent, we write it as 1/f^2. 40f^(-2) = 40/f^2

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Simplify. Express your answer using positive exponents. $\newline$ $\frac{10f^6 \cdot 8f}{2f^9}$

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Grade 8

Multiply and divide powers: variable bases

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Q. Simplify. Express your answer using positive exponents.

\newline

\frac{10f^6 \cdot 8f}{2f^9}

Multiply and Combine Terms: Multiply the coefficients (numbers) and combine the $f$ terms using the product rule for exponents. $\newline$ The product rule states that when you multiply two powers with the same base, you add the exponents. $\newline$ $10f^6 \times 8f = 80f^{6+1} = 80f^7$
Divide by $2f^9$ : Divide the new expression by $2f^9$ using the quotient rule for exponents. $\newline$ The quotient rule states that when you divide two powers with the same base, you subtract the exponents. $\newline$ $(80f^7)/2f^9 = (80/2)f^{(7-9)} = 40f^{-2}$
Express with Positive Exponents: Express the answer using positive exponents. $\newline$ To express $f^{-2}$ with a positive exponent, we write it as $1/f^2$ . $\newline$ $40f^{-2} = 40/f^2$