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}}\\) number of factors of 10 in \\(10^{6}\\): \\(square\\) number of factors of 10 in \\(10^{4}\\): \\(?\\)

Explanation:

Step1: Identify factors in $10^6$

The exponent tells the number of 10 factors: $10^6 = 10 \times 10 \times 10 \times 10 \times 10 \times 10$, so there are 6 factors.

Step2: Identify factors in $10^4$

The exponent tells the number of 10 factors: $10^4 = 10 \times 10 \times 10 \times 10$, so there are 4 factors.

Step3: Simplify the quotient

Use the quotient rule for exponents: $\frac{10^m}{10^n} = 10^{m-n}$
$\frac{10^6}{10^4} = 10^{6-4} = 10^2$

Answer:

Number of factors of 10 in $10^6$: 6
Number of factors of 10 in $10^4$: 4
The quotient as a single power of 10: $10^2$