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Which expression is equivalent to 100,000 * 10^(-4) * 10^(-5) * 10^(-6) * 10^(-7)?

A) 0.00000000001
B) 1
C) 0.00001
D) 100,000

1 Answer

3 votes

Final answer:

The equivalent expression for 100,000 * 10^(-4) * 10^(-5) * 10^(-6) * 10^(-7) is 1 x 10^(-17), which does not match any of the provided multiple-choice options.

Step-by-step explanation:

The expression 100,000 * 10^(-4) * 10^(-5) * 10^(-6) * 10^(-7) involves multiplying a base number (100,000) by several powers of 10 with negative exponents. To find the equivalent expression, we can add the exponents together. The base of 10 simplifies this process because adding the exponents is the same as multiplying the powers of 10.

First, let's add the exponents: -4 + (-5) + (-6) + (-7) = -22. Now, we apply this exponent to the base 10: 10^(-22). Multiplying this with 100,000 is the same as moving the decimal point 5 places to the right (because 100,000 = 10^5), but since the exponent is negative, we're actually moving the decimal 22 places to the left.

100,000 * 10^(-22) = 10^5 * 10^(-22) = 10^(5-22) = 10^(-17).

Thus, the equivalent expression is written in standard form as 1 x 10^(-17), which is not represented by any of the choices A, B, C, or D provided in the question.

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