Subjects algebra

Exponentiation 259Ce7

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1. **State the problem:** Calculate the value of $10^{2.37}$. 2. **Formula used:** The expression is an exponential function where the base is 10 and the exponent is 2.37. 3. **Explanation:** To evaluate $10^{2.37}$, we use the property of exponents that $a^b = \exp(b \ln a)$. 4. **Intermediate work:** $$10^{2.37} = \exp(2.37 \times \ln 10)$$ Since $\ln 10 \approx 2.302585$, $$10^{2.37} = \exp(2.37 \times 2.302585) = \exp(5.45612)$$ 5. **Final evaluation:** Using a calculator, $$10^{2.37} \approx 234.422$$ Thus, the value of $10^{2.37}$ is approximately 234.422.