A^1⁰×a^1⁵×(a^⁶)^⁸×(2a)^12/(a^2⁸:a^12)×(2a^⁴)^11×a^23 +a⁰ при a=3

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вопрос

Let's plug in a=3 into the expression:

3^10 × 3^15 × (3^6)^8 × (23)^12 / (3^28 : 3^12) × (23^4)^11 × 3^23 + 3^0

Simplify each term:

3^10 × 3^15 × 3^48 × 6^12 / 3^16 × 6^11 × 3^23 + 1

3^73 × 6^12 / 3^16 × 6^11 × 3^23 + 1

Now, simplify the terms further:

3^(73-16) × 6^(12-11) × 3^(23) + 1

3^57 × 6 × 3^23 + 1

From here, we can simplify even further:

3^57 × 6 × 3^23 + 1 = 3^57 × 2 × 3^23 + 1 = 2 × 3^80 + 1

Evaluating this expression with a=3:

2 × 3^80 + 1 = 2 × 3^80 + 1

Approximately, the value is:

2 × 3^80 + 1 ≈ 8.488 × 10^38 + 1 ≈ 8.488 × 10^38 + 1

Therefore, the final output is approximately 8.488 × 10^38 + 1.