Subjects algebra

Expression Simplification 50C3Ff

Step-by-step solutions with LaTeX - clean, fast, and student-friendly.

Use the AI math solver

1. **State the problem:** Simplify the expression $$\left( \frac{(x^{82}_{282}[292(2973)] + \text{Pentres}) * 2820^{917}}{[\![2937293828293882828382]\!]}\right) \% 99 + \sqrt[7]{\pi^{42}} - e^{i\pi}$$. 2. **Analyze components:** - The term $x^{82}_{282}[292(2973)] + \text{Pentres}$ is symbolic and cannot be simplified without definitions. - The denominator $[\![2937293828293882828382]\!]$ appears as a large constant or notation, no simplification possible. - The modulo operation $\% 99$ applies to the fraction, but since numerator and denominator are symbolic, we cannot compute it. - The term $\sqrt[7]{\pi^{42}}$ simplifies using exponent rules: $$\sqrt[7]{\pi^{42}} = \pi^{\frac{42}{7}} = \pi^6$$. - The term $e^{i\pi}$ is Euler's formula: $$e^{i\pi} = -1$$. 3. **Rewrite expression with simplifications:** $$\left( \frac{(x^{82}_{282}[292(2973)] + \text{Pentres}) * 2820^{917}}{[\![2937293828293882828382]\!]}\right) \% 99 + \pi^6 - (-1)$$ 4. **Simplify further:** $$= \left( \frac{(x^{82}_{282}[292(2973)] + \text{Pentres}) * 2820^{917}}{[\![2937293828293882828382]\!]}\right) \% 99 + \pi^6 + 1$$ 5. **Conclusion:** Without numeric values or definitions for symbolic parts, the expression simplifies to: $$\boxed{\left( \frac{(x^{82}_{282}[292(2973)] + \text{Pentres}) * 2820^{917}}{[\![2937293828293882828382]\!]}\right) \% 99 + \pi^6 + 1}$$ This is the simplest form given the information.