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Chapter 5: Problem 32

Write each number without exponents. $$ 8.56 \times 10^{0} $$

Short Answer

Expert verified
8.56

Step by step solution

01

- Understand the Exponent

The exponent indicates the power of ten that the base number is multiplied by. In this case, the exponent is 0.
02

- Apply the Exponent

Any number raised to the power of 0 is 1. So, we consider the multiplier of 10 raised to the power of 0.
03

- Simplify the Expression

Multiply 8.56 by 10 raised to the power of 0. This results in: \[8.56 \times 10^{0} = 8.56 \times 1 = 8.56\] Thus, the number without exponents is 8.56.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Exponents
Exponents are a way to represent repeated multiplication of the same number. For example, when you see an expression like \(10^3\), it means you should multiply 10 by itself three times: \(10 \times 10 \times 10\).
In mathematical terms, the exponent is the small number placed to the upper right of the base number. In this example, 10 is the base and 3 is the exponent.
  • The base tells you which number is being multiplied.
  • The exponent tells you how many times to multiply that base number by itself.
Understanding this basic relationship between the base and the exponent is crucial.
Multiplication
Multiplication is one of the core operations in math. It involves combining groups of equal sizes. When it comes to exponents, multiplication plays a key role.
For instance, in the case of \(8.56 \times 10^0\), you multiply 8.56 by the result of \(10^0\). Remember:
  • When you multiply a number by 1, it remains unchanged.
  • When you multiply by 0, the result is always 0. But be careful: exponents follow different rules compared to regular multiplication.
To multiply by an exponent, you must first calculate the power, then multiply that result by your given number.
Simplification
Simplification makes complex expressions easier to understand and work with. In our example, we start with \(8.56 \times 10^0\).
The exponent rule that any number raised to the power of 0 equals 1 simplifies our task. This means:
\[10^0=1\]
So \(8.56 \times 10^0\) becomes \(8.56 \times 1\).
Any number multiplied by 1 stays the same, making our final simplified answer 8.56. Simplification helps in breaking down complex problems into simpler parts.
Powers of Ten
Powers of ten are specific exponents where the base is 10. They simplify a lot of calculations, especially when dealing with large or small numbers.
For example:
  • \(10^1 = 10\)
  • \(10^2 = 100\)
  • \(10^3 = 1,000\)
Similarly, negative exponents represent division:
  • \(10^{-1} = 0.1\)
  • \(10^{-2} = 0.01\)
The key rule is \(10^0\) always equals 1. Whether the exponent is positive, negative, or 0, this rule helps you quickly find the value of these expressions and apply them in larger calculations.

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Most popular questions from this chapter

Use scientific notation to calculate the answer to each problem. In 2007 , the state of Minnesota had about \(7.9 \times 10^{4}\) farms with an average of \(3.5 \times 10^{2}\) acres per farm. What was the total number of acres devoted to farmland in Minnesota that year?

Use scientific notation to calculate the answer to each problem. The body of a 150 -lb person contains about \(2.3 \times 10^{-4} 1 b\) of copper. How much copper is contained in the bodies of 1200 such people?

List all positive integer factors of each number. $$ 18 $$

Write each number in scientific notation. $$ -0.01234 $$

Perform each division using the "long division" process. $$ \frac{27 r^{4}-36 r^{3}-6 r^{2}+26 r-24}{3 r-4} $$
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