Question

which expression is equivalen t to the follwoing (a^)^2 -2a^-3b^4

Answer 1

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:
\[
\frac{a^5 - 2b^4}{a^3}
\]