Why is the expression $(((30 / 2) / 2) / 2)$ same as $30 / 2^3$

Question

Why is the expression $$(((30 / 2) / 2) / 2)$$ same as $$30 / 2^3$$

Answer 1

Note that

$$\begin{align} \color{blue}{(30/2)/2} &= \frac{30}{2}\times \frac{1}{2}\\ &=\color{teal}{ \frac{30}{2^2}} \end{align}.$$

Hence $$\begin{align} (\color{blue}{(30/2)/2})/2 &= \color{teal}{\left(\frac{30}{2^2}\right)}\bigg{/}2\\ &= \frac{30}{2^2}\times \frac{1}{2}\\ &= \frac{30}{2^3}. \end{align}$$

Answer 2

$$30\div2\div2\div2=\frac{30}{2}\div2\div2$$ $$=\frac{30}{2^2}\div2$$ $$=\frac{30}{2^3}$$

Answer 3

Recall:

$(30/2)=30\cdot \dfrac{1}{2};$

$((30/2)/2)=(30\cdot \dfrac{1}{2})\cdot \dfrac{1}{2};$

$(30/2)/2)/2=$

$((30 \cdot \dfrac{1}{2})\cdot \dfrac{1}{2})\cdot \dfrac{1}{2}= 30 \cdot (\dfrac{1}{2})^3= \dfrac{30}{2^3}$

Used: Associative law of multiplication.