A^5-a^-3

To simplify the expression \( a^5 - a^{-3} \), we can express everything in terms of positive exponents.

Recall that \( a^{-n} = \frac{1}{a^n} \). Thus, we can rewrite the expression:

\[ a^5 - a^{-3} = a^5 - \frac{1}{a^3} \]

To combine the two terms, we can find a common denominator. The least common denominator (LCD) is \( a^3 \):

\[ = \frac{a^5 \cdot a^3}{a^3} - \frac{1}{a^3} \]

This simplifies to:

\[ = \frac{a^8 - 1}{a^3} \]

So, the simplified form of the expression \( a^5 - a^{-3} \) is:

\[ \frac{a^8 - 1}{a^3} \]

If you need further assistance or clarification, feel free to ask!