Verified Answer :

  • Identify the repeated factor as 10, which appears 4 times in the expression.
  • Apply the definition of exponents to write the repeated multiplication as \(10^4\).
  • Multiply the coefficient 6 by this exponential form to obtain the final result.
  • The final expression is \(\boxed{6 \times 10^4}\).

Explanation

  1. Analyze the Expression

The expression given is \(6 \times 10 \times 10 \times 10 \times 10\). We are asked to represent this expression using an exponent. An exponent tells us how many times a base number is multiplied by itself. In this expression, the number 10 is being multiplied by itself multiple times, while the 6 acts as a coefficient.

  1. Identify the Exponential Form

To express the multiplication of the same factor using exponents, we count how many times that factor appears. Here, 10 is multiplied by itself 4 times: \[10 \times 10 \times 10 \times 10 = 10^4\] This is the exponential form of the repeated multiplication of 10.

  1. Conclusion

Now, we substitute the exponential form back into the original expression: \[6 \times 10 \times 10 \times 10 \times 10 = 6 \times 10^4\] The entire expression can therefore be written as \(6 \times 10^4\). This is a standard way to write numbers in scientific notation, which is often used to represent large values concisely. The final answer is \(\boxed{6 \times 10^4}\).

Examples

Exponents are incredibly useful in science and everyday life for representing very large numbers without writing many zeros. For example, the distance from the Earth to the Sun is approximately 150,000,000 kilometers. Instead of writing out all the zeros, we can write this as \(1.5 \times 10^8\) km. This notation makes calculations with extremely large or small numbers much easier to handle and read.

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