# (9.5×10^{11})+(6.3×10^{9})

Question
Algebra foundations
$$\displaystyle{\left({9.5}×{10}^{{{11}}}\right)}+{\left({6.3}×{10}^{{{9}}}\right)}$$

2021-03-10
To simplify this expression you just need to modify one of the terms so it has the same power of ten as the other. I find it easier to lower a power than raise it so we'll use the fact that $$\displaystyle{10}^{{{11}}}={100}×{10}^{{{9}}}.$$ Then
$$\displaystyle{9.5}×{\left({10}^{{{11}}}\right)}+{6.3}×{10}^{{{9}}}={9.5}×{100}×{\left({10}^{{{9}}}\right)}+{6.3}×{10}^{{{9}}}={950}×{\left({10}^{{{9}}}\right)}+{6.3}×{10}^{{{9}}}={\left({950}+{6.3}\right)}×{10}^{{{9}}}={956.3}×{10}^{{{9}}}$$
Note that if your course has recently covered maintaining significant figures, then you'll need to round this to the tens place. Hence your answer will instead be $$\displaystyle{950}×{10}^{{{9}}}={9.5}×{10}^{{{11}}}$$

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