Simplify the expression:

\[ 3^{-(4a+1)} - 3^{-(4a-1)} + 3^{-4a} \]

3 − ( 4 a + 1 ) − 3 − ( 4 a − 1 ) + 3 − 4 a = 3 − 4 a − 1 − 3 − 4 a + 1 + 3 − 4 a = = 3 − 4 a ∗ 3 − 1 − 3 − 4 a ∗ 3 1 + 3 − 4 a = 3 − 4 a ( 3 − 1 − 3 + 1 ) = 3 − 4 a ∗ ( 3 1 ​ − 2 ) = = 3 − 4 a ∗ ( − 1 3 2 ​ ) = 3 − 4 a ∗ ( − 3 5 ​ ) = 3 − 4 a ∗ ( − 5 ) ∗ 3 1 ​ = − 5 ∗ 3 − 4 a ∗ 3 − 1 = = − 5 ∗ 3 − 4 a + ( − 1 ) = − 5 ∗ 3 − 4 a − 1

Answered by Lilith | 2024-06-10

The expression 3 − ( 4 a + 1 ) − 3 − ( 4 a − 1 ) + 3 − 4 a simplifies to − 3 4 a + 1 5 ​ . This was achieved by factoring out common terms and simplifying the remaining expression. The final result illustrates how exponent properties can help simplify expressions effectively.
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Answered by Lilith | 2025-01-15