Question

(0.001) to the power 1 by 3

Answer 1

Answer:

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

3

1

.

Given:

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

3

1

To find:

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

3

1

Solution:

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

3

1

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

1

. 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

1

will be \frac{1}{10}

10

1

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

3

1

3

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

3

1

=(

10

3

1

3

)

3

1

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

=

10

1

=0.1

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

3

1

is \bold{0.1}0.1