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MAXImum [283]
3 years ago
13

Describe the pattern in the numbers. Write the next number in the pattern. 1, 2/3, 1/3, 0

Mathematics
1 answer:
olga2289 [7]3 years ago
6 0

Answer:

-1/3

Step-by-step explanation:

its subtracting 1/3 every time

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Which expressions are equivalent to \dfrac{4^{-3}}{4^{-1}} 4 −1 4 −3 ​ start fraction, 4, start superscript, minus, 3, end super
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Answer:

\dfrac{4^{-3}}{4^{-1}} = \dfrac{4^{1}}{4^{3}}

\dfrac{4^{-3}}{4^{-1}} = \dfrac{1}{4^{2}}

Step-by-step explanation:

Given

\dfrac{4^{-3}}{4^{-1}}

Required

Choose equivalent expressions

Choosing the first answer:

\dfrac{4^{-3}}{4^{-1}}

Split expressions

4^{-3} * \frac{1}{4^{-1}}

Apply laws of indices: (a^{-b} = \frac{1}{a^b})

\frac{1}{4^3} * \frac{1}{4^{-1}}

Apply laws of indices: (a^{-b} = \frac{1}{a^b})

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\frac{1}{4^3} * \frac{4^1}{1}

\frac{4^1}{4^3}

Hence:

\dfrac{4^{-3}}{4^{-1}} = \dfrac{4^{1}}{4^{3}}

Choosing the second:

\dfrac{4^{-3}}{4^{-1}}

Apply law of indices: (\frac{a^m}{a^n} = a^{m-n})

So,

\dfrac{4^{-3}}{4^{-1}} = 4^{-3-(-1)}

\dfrac{4^{-3}}{4^{-1}} = 4^{-3+1)}

\dfrac{4^{-3}}{4^{-1}} = 4^{-2}

Apply law of indices: (a^{-b} = \frac{1}{a^b})

So:

\dfrac{4^{-3}}{4^{-1}} = \dfrac{1}{4^{2}}

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