question :
$a = 1.2 \times 10^{101}$
$b = 2 \times 10^{34}$
showing all your working, calculate, giving your answer in standard form, the value of $b^3 - a$ ____________________________________________________________________
I would like to know how to solve this step by step. I started off like this $$(2 \times 10^{34})^3 - 2.1\times 10^{101}$$ I opened the brackets with my next step being $$8 \times 10^{102} - 1.2 \times 10^{101}$$ I guess this is wrong, and I don't know what to do next. It doesn't lead to the answer in the marking scheme $7.88 \times 10^{102}$
\begin{align} a &= 1.2 \times 10^{101} \\ b &= 2 \times 10^{34} \\ b^3-a &= (2 \times 10^{34})^3 - \color{red}{1.2} \times 10^{101} \tag{You've carelessly written 2.1.} \\ &= 8 \times 10^{102} - 0.12 \times 10^{102} \\ &= (8 - 0.12) \times 10^{102} \\ &= 7.88 \times 10^{102} \end{align}