Questions: Simplify. 16 a^7 b^5 / -3 a^6 b^2

Simplify. 16 a^7 b^5 / -3 a^6 b^2
Transcript text: Simplify. \[ \frac{16 a^{7} b^{5}}{-3 a^{6} b^{2}} \]
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Solution

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Solution Steps

To simplify the given expression, we need to divide the coefficients and subtract the exponents of like bases according to the laws of exponents.

Step 1: Divide the Coefficients

To simplify the expression \(\frac{16 a^{7} b^{5}}{-3 a^{6} b^{2}}\), we first divide the coefficients: \[ \frac{16}{-3} = -\frac{16}{3} \]

Step 2: Subtract the Exponents of \(a\)

Next, we subtract the exponents of \(a\): \[ a^{7} / a^{6} = a^{7-6} = a^{1} = a \]

Step 3: Subtract the Exponents of \(b\)

Then, we subtract the exponents of \(b\): \[ b^{5} / b^{2} = b^{5-2} = b^{3} \]

Step 4: Combine the Results

Combining the results from the previous steps, we get: \[ -\frac{16}{3} \cdot a \cdot b^{3} = -\frac{16 a b^{3}}{3} \]

Final Answer

\[ \boxed{-\frac{16 a b^{3}}{3}} \]

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