In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 2^3.4

Verified step by step guidance

1. Identify the expression to evaluate: \$2^{3.4}$.
2. Recall that \(a^b\) means \(a\) raised to the power of \(b\), where \(a=2\) and \(b=3.4\) in this case.
3. Use a calculator to compute \$2^{3.4}\(. Most calculators have a power function, often labeled as \)x^y$ or \(\hat{}\).
4. Enter 2, then use the power function, and then enter 3.4 to get the approximate value.
5. Round the result to three decimal places as instructed.

Key Concepts

Exponents and Powers

Exponents indicate how many times a base number is multiplied by itself. For example, 2^3 means 2 multiplied by itself 3 times (2 × 2 × 2). Understanding how to interpret and work with exponents is essential for evaluating expressions like 2^3.4.

Decimal Exponents

Decimal exponents represent roots and fractional powers, extending the idea of integer exponents. For instance, 2^3.4 means 2 raised to a power between 3 and 4, which can be calculated using logarithms or a calculator. This concept helps in approximating values that are not whole-number powers.

Rounding to a Specified Decimal Place

Rounding is the process of limiting a number to a certain number of decimal places for simplicity and clarity. Rounding to three decimal places means keeping three digits after the decimal point and adjusting the last digit based on the next digit. This ensures the answer is precise yet manageable.