To simplify the expression \((a^2) - 2a^{-3}b^4\), we can look for equivalent expressions by rewriting \(a^{-3}\) and simplifying it further.
Starting with the original expression: \[ a^2 - 2a^{-3}b^4 \]
We recognize that \(a^{-3} = \frac{1}{a^3}\), so we can rewrite the term \(2a^{-3}b^4\) as: \[ 2a^{-3}b^4 = \frac{2b^4}{a^3} \]
Thus, the original expression can be rewritten as: \[ a^2 - \frac{2b^4}{a^3} \]
To combine these terms into a single fraction, we can express \(a^2\) with a common denominator: \[ a^2 = \frac{a^5}{a^3} \quad (\text{since } a^2 = \frac{a^2 \cdot a^3}{a^3} = \frac{a^5}{a^3}) \]
Now substituting this back: \[ \frac{a^5}{a^3} - \frac{2b^4}{a^3} = \frac{a^5 - 2b^4}{a^3} \]
So, the expression is now: \[ \frac{a^5 - 2b^4}{a^3} \]
Therefore, an equivalent expression for \( (a^2) - 2a^{-3}b^4 \) is: \[ \frac{a^5 - 2b^4}{a^3} \]
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