Question

What does 4^8/4^-2 equal?

Answer 1

Answer:

Hello there I'm Ashlynn It's lovely to meet you

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(4^8) / (4^(-2)) = 1, 048, 576

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Answer 2

Answer:

4^10 (base 4)

2^20 (base 2)

Step-by-step explanation:

Law of Exponent:

$\displaystyle \large{ \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} }$

Compare:

$\displaystyle \large{ \frac{ {a}^{m} }{ {a}^{n} } = \frac{ {4}^{8} }{ {4}^{ - 2} } }$

• a = 4
• m = 8
• n = -2

Therefore:

$\displaystyle \large{ \frac{ {4}^{8} }{ {4}^{ - 2} } = {4}^{8 - ( - 2)} } \\ \displaystyle \large{ \frac{ {4}^{8} }{ {4}^{ - 2} } = {4}^{8 + 2} } \\ \displaystyle \large{ \frac{ {4}^{8} }{ {4}^{ - 2} } = {4}^{10} }$

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:

$\displaystyle \large{ {4}^{10} = { ({2}^{2}) }^{10} }$

Law of Exponent II

$\displaystyle \large{ { ({a}^{m} )}^{n} = {a}^{m \times n} }$

Apply the law:

$\displaystyle \large{ {4}^{10} = { ({2}^{2}) }^{10} } \\ \displaystyle \large{ {4}^{10} = {2}^{20} }$

Thus, in base 2 form, it's 2^20