1. Intro to Stats and Collecting Data
Intro to Stats
1:54 minutesProblem 1.CRE.10
Textbook Question
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.
(8)^12
Verified step by step guidance1
Identify the base and the exponent in the expression. Here, the base is 8 and the exponent is 12.
Understand that the expression 8^12 means multiplying the base, 8, by itself 12 times.
Use the properties of exponents to simplify calculations if possible. For example, you can break down the exponentiation into smaller parts, such as (8^6)^2, to make calculations easier.
Calculate the power of 8 raised to 12 using a calculator or by performing successive multiplications.
Convert the result from scientific notation to an ordinary number if necessary. Ensure the final result is expressed as a whole number without using scientific notation.
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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 uses powers of ten to simplify numbers, such as 1.23E5 for 123,000. Understanding scientific notation is crucial for converting results into ordinary numbers.
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Exponentiation
Exponentiation is a mathematical operation involving two numbers, the base and the exponent. It represents repeated multiplication of the base by itself, such as 8^12, which means multiplying 8 by itself 12 times. Grasping this concept is essential for performing calculations involving powers.
Conversion to Ordinary Numbers
Converting scientific notation to ordinary numbers involves understanding the placement of the decimal point based on the exponent. Positive exponents shift the decimal to the right, while negative exponents shift it to the left. This conversion is necessary to express results in a standard numerical form.
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