Question

you can use similar patterns to divide powers with the same base. write the quotient shown below as a single power of 10. how many factors of 10 are in each power? \\(\frac{10^6}{10^4}=\frac{10\cdot10\cdot10\cdot10\cdot10\cdot10}{10\cdot10\cdot10\cdot10}\\) number of factors of 10 in \\(10^6\\): 6 number of factors of 10 in \\(10^4\\): 4 how many factors of 10 are in the quotient? number of factors of 10 in \\(\frac{10^6}{10^4}\\):

Explanation:

Step1: Subtract exponents (same base)

When dividing powers with the same base, subtract the denominator exponent from the numerator exponent: $6 - 4 = 2$

Step2: Relate to factor count

The result of the subtraction equals the number of 10 factors in the quotient.

Answer:

2