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Chapter 9: Problem 55

Evaluate. $$ 10^{5} $$

Short Answer

Expert verified
100000

Step by step solution

01

Understand the notation

The notation \(10^{5}\) means 10 raised to the power of 5. This indicates that we need to multiply 10 by itself 5 times.
02

Multiply 10 by itself

Calculate \(10 \times 10 \times 10 \times 10 \times 10\).
03

Perform multiplication step-by-step

\(10 \times 10 = 100\), then \(100 \times 10 = 1000\), then \(1000 \times 10 = 10000\), and finally \(10000 \times 10 = 100000\).
04

Write the final result

So, \(10^{5} = 100000\).

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Key Concepts

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

Power of a Number
In mathematics, the 'power of a number' refers to how many times you multiply the number by itself. This concept is also known as 'exponentiation'.

When you see an expression like \(10^{5}\), the small number (called the 'exponent') tells you the number of times to use the larger number (the 'base') in a multiplication.

For example, in \(10^{5}\):
  • 10 is the base.
  • 5 is the exponent, indicating that we multiply 10 by itself 5 times.
Therefore, calculating \(10^{5}\) results in:
\[10 \times 10 \times 10 \times 10 \times 10 = 100000\]\
This is how the power of a number works!
Multiplication
Multiplication is a key mathematical operation that involves adding a number to itself a certain number of times. This is especially important when working with exponents.

In the example of \(10^{5}\), we need to multiply 10 by itself repeatedly:
  • First, calculate \(10 \times 10 = 100\).
  • Next, multiply the result by 10 again: \(100 \times 10 = 1000\).
  • Continue this process: \(1000 \times 10 = 10000\).
  • Finally, \(10000 \times 10 = 100000\).
Using step-by-step multiplication, we discover that \(10^{5} = 100000\).

This method demonstrates how multiplication helps us understand and solve exponent problems efficiently.
Notation
Mathematical notation is a powerful tool to communicate ideas precisely and efficiently. When dealing with exponents, notation helps to clearly express the relationship between the base and the exponent.

In the expression \(10^{5}\):
  • '10' is the base number, which is the number we will multiply.
  • '5' is the exponent, which tells us the number of times to perform the multiplication.
This notation simplifies complex mathematical operations.
Instead of writing '10 multiplied by itself 5 times', we simply write \(10^{5}\).

Understanding notation lets us quickly grasp and solve exponent problems.

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