Subjects algebra

Sqrt Exponential C867E2

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

Use the AI math solver

1. **State the problem:** Calculate the value of $\sqrt{3,312,400} \times e^{-\ln(130)}$. 2. **Recall formulas and rules:** - The square root of a number $a$ is written as $\sqrt{a}$. - The exponential and logarithm functions satisfy the identity $e^{-\ln(x)} = \frac{1}{e^{\ln(x)}} = \frac{1}{x}$. 3. **Calculate the square root:** $$\sqrt{3,312,400} = 1820$$ 4. **Simplify the exponential term:** $$e^{-\ln(130)} = \frac{1}{130}$$ 5. **Multiply the results:** $$1820 \times \frac{1}{130} = \frac{1820}{130}$$ 6. **Simplify the fraction:** $$\frac{1820}{130} = \frac{\cancel{1820}^{14} \times 130}{\cancel{130}} = 14$$ 7. **Final answer:** $$14$$