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? number of factors of 10 in (10^6): 6 number of factors of 10 in (10^4): 4 (\frac{10^6}{10^4}=\frac{10cdot10cdot10cdot10cdot10cdot10}{10cdot10cdot10cdot10}=\frac{10}{10}cdot\frac{10}{10}cdot\frac{10}{10}cdot\frac{10}{10}cdot10cdot10 = 1cdot1cdot1cdot1cdot10cdot10 = 10cdot10) how many factors of 10 are in the quotient? number of factors of 10 in (\frac{10^6}{10^4}): 2 now, write the quotient as a single power. (\frac{10^6}{10^4}=) dropdown with (10^2), (10^4), (10^{10}), (10^{24}), (10^{10}) (maybe a typo)

Explanation:

Step1: Recall exponent division rule

For same base $a^m/a^n = a^{m-n}$

Step2: Substitute values $a=10, m=6, n=4$

$\frac{10^6}{10^4}=10^{6-4}$

Step3: Calculate the exponent

$10^{6-4}=10^2$

Answer:

$10^2$