To simplify the expression \(-\frac{5a^3b^4c^{-2}}{3a^{-4}b^0c^3}\), we can break it down step-by-step using the properties of integer exponents.
-
Simplify the coefficients: The coefficient in the numerator is \(-5\) and in the denominator is \(3\). Thus, we have: \[ -\frac{5}{3} = -\frac{5}{3} \]
-
Simplify \(a\) terms: We apply the exponent rule \(a^m/a^n = a^{m-n}\): \[ a^3/a^{-4} = a^{3 - (-4)} = a^{3 + 4} = a^7 \]
-
Simplify \(b\) terms: Recall that \(b^0 = 1\), hence: \[ b^4/b^0 = b^4/1 = b^4 \]
-
Simplify \(c\) terms: Again using the exponent rule: \[ c^{-2}/c^3 = c^{-2 - 3} = c^{-5} \]
Putting it all together, we combine the results: \[ -\frac{5}{3} \cdot a^7 \cdot b^4 \cdot c^{-5} \]
To express \(c^{-5}\) in the denominator: \[ c^{-5} = \frac{1}{c^5} \]
Thus, the expression becomes: \[ -\frac{5}{3} \cdot \frac{a^7b^4}{c^5} \]
In final simplified form, we write it as: \[ -\frac{5a^7b^4}{3c^5} \]
Therefore, the simplified expression is: \[ -\frac{5a^7b^4}{3c^5} \]
2 answers