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Which expressions are equivalent to \dfrac{1}{5}\cdot \dfrac{1}{5}\cdot \dfrac{1}{5}\cdot \dfrac{1}{5}

Question

Which expressions are equivalent to \dfrac{1}{5}\cdot \dfrac{1}{5}\cdot \dfrac{1}{5}\cdot \dfrac{1}{5}

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Solution

The given expression is a multiplication of the fraction 1/5 four times. This can be written in several equivalent forms:

  1. As a power: (15)4(\dfrac{1}{5})^4 This means "1/5 multiplied by itself 4 times".

  2. As a decimal: 0.240.2^4 This is because 1/5 is equivalent to 0.2.

  3. As a fraction: 1625\dfrac{1}{625} This is because 5^4 = 625, so (1/5)^4 = 1/625.

  4. As a decimal: 0.00160.0016 This is because 1/625 is equivalent to 0.0016.

So, the expressions equivalent to 15151515\dfrac{1}{5}\cdot \dfrac{1}{5}\cdot \dfrac{1}{5}\cdot \dfrac{1}{5} are (15)4(\dfrac{1}{5})^4, 0.240.2^4, 1625\dfrac{1}{625}, and 0.00160.0016.

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