In Exercises 9–12, the given expressions are designed to yield results expressed in a form of scientific notation. For example, the calculator-displayed result of 1.23E5 can be expressed as 123,000, and the result of 1.23E-4 can be expressed as 0.000123. Perform the indicated operation and express the result as an ordinary number that is not in scientific notation.

(0.2)^12

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Understand the problem: You need to calculate the value of (0.2)^12 and express the result as an ordinary number, not in scientific notation.

Recognize that (0.2)^12 involves exponentiation, where 0.2 is the base and 12 is the exponent. This means you multiply 0.2 by itself 12 times.

Use a calculator to perform the operation: Enter 0.2 and use the exponentiation function to raise it to the power of 12.

Once you have the result from the calculator, check if it is displayed in scientific notation. If it is, convert it to an ordinary number by moving the decimal point according to the exponent.

Write down the final result as an ordinary number, ensuring that it is not in scientific notation, and verify the accuracy of your conversion.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Scientific Notation

Scientific notation is a way of expressing numbers that are too large or too small to be conveniently written in decimal form. It is typically used in scientific and engineering contexts. A number is expressed in the form of a × 10^n, where 1 ≤ a < 10 and n is an integer. For example, 1.23E5 represents 123,000.

Exponentiation

Exponentiation is a mathematical operation involving two numbers, the base and the exponent. The operation is written as b^n, where b is the base and n is the exponent, meaning b is multiplied by itself n times. For example, (0.2)^12 means multiplying 0.2 by itself 12 times, which is crucial for solving the given expression.

Converting Scientific Notation to Decimal

Converting scientific notation to a decimal involves moving the decimal point to the right for positive exponents or to the left for negative exponents, based on the power of ten. For instance, 1.23E-4 is converted to 0.000123 by moving the decimal point four places to the left, which is essential for expressing results in ordinary numbers.

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