Answer:

0.1 is the value of \bold{(0.001)^{\frac{1}{3}}.}(0.001)

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.

Given:

(0.001)^{\frac{1}{3}}(0.001)

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To find:

Value of (0.001)^{\frac{1}{3}}(0.001)

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Solution:

To find the value of (0.001)^{\frac{1}{3}}(0.001)

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Procedure to solve the given decimal:

First express the decimal EXPANSION into FRACTION to convert 0.001 into fraction observing the decimal after the point there are three numbers so it will become\frac{1}{1000}

1000

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. In the question it is given that the decimal RAISE to the power 1/3 it means taking cube root. The cube root of \frac{1}{1000}

1000

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will be \frac{1}{10}

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then converting the given fraction into decimal it is 0.1.

0.001=\frac{1}{1000}=\frac{1 \TIMES 1 \times 1}{10 \times 10 \times 10}=\frac{1^{3}}{10^{3}}0.001=

1000

1

=

10×10×10

1×1×1

=

10

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3

(0.001)^{\frac{1}{3}}=\left(\frac{1^{3}}{10^{3}}\right)^{\frac{1}{3}}(0.001)

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=(

10

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3

)

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\begin{gathered}\begin{array}{l}{=\frac{1}{10}} \\ {=0.1}\END{array}\end{gathered}

=

10

1

=0.1

The value of \bold{(0.001)^{\frac{1}{3}}}(0.001)

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is \bold{0.1}0.1