In Exercises 1–10, approximate each number using a calculator. Round your answer to three decimal places. 4^-1.5

Key Concepts

Exponents and Powers

Exponents represent repeated multiplication of a base number. In the expression 4^-1.5, the negative exponent indicates the reciprocal of the base raised to the positive exponent. Thus, 4^-1.5 can be rewritten as 1/(4^1.5), which simplifies the calculation process.

Rounding Numbers

Rounding is the process of adjusting a number to a specified degree of accuracy, often to make it simpler or easier to work with. In this case, rounding to three decimal places means keeping three digits after the decimal point and adjusting the last digit based on the value of the next digit.

Using a Calculator for Exponential Functions

Calculators can efficiently compute exponential functions, including those with fractional or negative exponents. To find 4^-1.5, one would input the base and exponent into the calculator, which will provide a decimal approximation that can then be rounded as required.