Evaluate 0.3^3

 Evaluate.

$0.3^3 =$0, point, 3, cubed, equals 

Hint #11 / 3

An exponent tells us how many factors of the base we should multiply to find the value of an expression.

For example, we can take the power of a decimal like this:

$\begin{aligned} \maroonD{0.5}^\blueE{3} &= \maroonD{0.5} \cdot \maroonD{0.5} \cdot \maroonD{0.5} \\\\ &=0.125 \end{aligned}$

Hint #22 / 3

$\begin{aligned} 0.3^3 &= 0.3 \cdot 0.3 \cdot 0.3 \\\\ &=0.027 \end{aligned}$

Since $0.3$0, point, 3 is three tenths, we can use fractions instead:

$\begin{aligned} 0.3^3 &= \dfrac{3}{10} \cdot \dfrac{3}{10} \cdot \dfrac{3}{10} \\\\ &=\dfrac{3 \cdot 3 \cdot 3}{10 \cdot 10 \cdot 10} \\\\ &=\dfrac{27}{1{,}000} \\\\ &=0.027 &&\gray{\text{(Twenty-seven thousandths)}} \end{aligned}$

Hint #33 / 3

$0.3^3 =0.027$