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Answered

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

Sagot :

VectorFundament120

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]

  • a = 4
  • m = 8
  • n = -2

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

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