Answer:
4^10 (base 4)
2^20 (base 2)
Step-by-step explanation:
Law of Exponent:
[tex] \displaystyle \large{ \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} }[/tex]
Compare:
[tex] \displaystyle \large{ \frac{ {a}^{m} }{ {a}^{n} } = \frac{ {4}^{8} }{ {4}^{ - 2} } }[/tex]
Therefore:
[tex] \displaystyle \large{ \frac{ {4}^{8} }{ {4}^{ - 2} } = {4}^{8 - ( - 2)} } \\ \displaystyle \large{ \frac{ {4}^{8} }{ {4}^{ - 2} } = {4}^{8 + 2} } \\ \displaystyle \large{ \frac{ {4}^{8} }{ {4}^{ - 2} } = {4}^{10} }[/tex]
Althought you didn't specific if I should leave answer as base 4 or base 2.
If you want the answer in base 2.
From:
[tex] \displaystyle \large{ {4}^{10} = { ({2}^{2}) }^{10} }[/tex]
Law of Exponent II
[tex] \displaystyle \large{ { ({a}^{m} )}^{n} = {a}^{m \times n} }[/tex]
Apply the law:
[tex] \displaystyle \large{ {4}^{10} = { ({2}^{2}) }^{10} } \\ \displaystyle \large{ {4}^{10} = {2}^{20} }[/tex]
Thus, in base 2 form, it's 2^20
