Math Problem Statement

Eric wanted to find out how many skin cells were lost in his hometown with a population of about 10^4 adults. He determined the expression (10^6)(10^4) would represent the approximate number of skin cells lost each day by all of the adults in his town. Which value represents the simplified expression?

Solution

The expression given is (106)×(104)(10^6) \times (10^4), and we are asked to simplify it.

When multiplying powers of 10, we apply the property of exponents:
10a×10b=10a+b10^a \times 10^b = 10^{a + b}

So: (106)×(104)=106+4=1010(10^6) \times (10^4) = 10^{6 + 4} = 10^{10}

The correct simplified expression is 101010^{10}, which corresponds to option D.


Would you like more details or have any other questions?

Here are some related questions to think about:

  1. How do you simplify expressions with exponents involving multiplication?
  2. What happens when you divide numbers with exponents of 10?
  3. How would the result change if the powers of 10 were negative?
  4. Can you apply the same rules of exponents to different bases, such as 2 or 5?
  5. How would you solve an expression with mixed multiplication and division of powers?

Tip: When multiplying powers of the same base, always add their exponents!

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Math Problem Analysis

Mathematical Concepts

Exponentiation
Properties of Exponents
Multiplication of Powers of 10

Formulas

10^a * 10^b = 10^(a+b)

Theorems

Laws of Exponents

Suitable Grade Level

Grades 6-8