Question

Evaluate(0.1)³ Solve (1/10)⁴

Answer 1

We can express the number 0.1 as the quotient 1/10, then we get:

$(0.1)^3=(\frac{1}{10})^3$

With quotients, we can distribute the power, and raise both the numerator and the denominator, like this:

$(\frac{1}{10})^3=\frac{1^3}{10^3}$

no matter what is the value of the power, every time you raise 1 to something, you get 1, then we get:

$\frac{1^3}{10^3}=\frac{1}{10^3}$

In this case, we have 10^3 in the denominator, this is the same as multiplying 10 3 times, like this:

$\frac{1}{10^3}=\frac{1}{10\times10\times10}=\frac{1}{100\times10}=\frac{1}{1000}$

Then:

$(0.1)^3=\frac{1}{1000}$

Similarly, with (1/10)^4:

$(\frac{1}{10})^4=\frac{1^4}{10^4}=\frac{1}{10^4}=\frac{1}{10\times10\times10\times10}=\frac{1}{10000}$