Questions: Simplify: 6a^6b^2c / 9a^3b^5 (A) 54a^9b^7c (B) 6a^2b^-3c / 9 (C) 2a^3c / 3b^3 (D) 2a^5c / 3b^7

Simplify: 6a^6b^2c / 9a^3b^5 (A) 54a^9b^7c (B) 6a^2b^-3c / 9 (C) 2a^3c / 3b^3 (D) 2a^5c / 3b^7
Transcript text: Simplify: $\frac{6 a^{6} b^{2} c}{9 a^{3} b^{5}}$ (A) $54 a^{9} b^{7} c$ (B) $\frac{6 a^{2} b^{-3} c}{9}$ (C) $\frac{2 a^{3} c}{3 b^{3}}$ (D) $\frac{2 a^{5} c}{3 b^{7}}$
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Solution

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Solution Steps

Step 1: Simplify the coefficients

Divide the coefficients \( \frac{6}{9} \) to simplify: \[ \frac{6}{9} = \frac{2}{3}. \]

Step 2: Simplify the variables with exponents

For the variable \( a \), subtract the exponents in the denominator from the exponents in the numerator: \[ a^{6} \div a^{3} = a^{6-3} = a^{3}. \]

For the variable \( b \), subtract the exponents in the denominator from the exponents in the numerator: \[ b^{2} \div b^{5} = b^{2-5} = b^{-3}. \]

The variable \( c \) remains unchanged since it only appears in the numerator: \[ c. \]

Step 3: Combine the simplified terms

Combine the simplified coefficients and variables: \[ \frac{2}{3} \cdot a^{3} \cdot b^{-3} \cdot c = \frac{2 a^{3} c}{3 b^{3}}. \]

Final Answer

\(\boxed{\frac{2 a^{3} c}{3 b^{3}}}\)

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