75a^2b^-2/5a^3b^-3

Answer 1

To simplify the expression \(\frac{75a^2b^{-2}}{5a^3b^{-3}}\), we can simplify the coefficients and the variables separately.

1. Simplify the coefficients: \[ \frac{75}{5} = 15 \]

2. Simplify the \(a\) terms: When dividing like bases, we subtract the exponents: \[ a^{2 - 3} = a^{-1} \]

3. Simplify the \(b\) terms: Similarly, we subtract the exponents for \(b\): \[ b^{-2 - (-3)} = b^{-2 + 3} = b^{1} = b \]

Putting it all together: \[ \frac{75a^2b^{-2}}{5a^3b^{-3}} = 15a^{-1}b \]

To express \(a^{-1}\) in a more standard form: \[ = \frac{15b}{a} \]

So, the simplified expression is: \[ \frac{15b}{a} \]