Simplify the following:
(4×107)(6×10−5)8×1010\dfrac{(4 \times 10^7)(6 \times 10^{-5})}{8 \times 10^{10}}8×1010(4×107)(6×10−5)
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Given,
⇒(4×107)(6×10−5)8×1010=4×6×107×10−58×1010=24×107+(−5)8×1010=24×1028×1010=3×102×10−10=3×102+(−10)=3×10−8.\Rightarrow \dfrac{(4 \times 10^7)(6 \times 10^{-5})}{8 \times 10^{10}} = \dfrac{4 \times 6 \times 10^7 \times 10^{-5}}{8 \times 10^{10}} \\[1em] = \dfrac{24 \times 10^{7 + (-5)}}{8 \times 10^{10}} = \dfrac{24 \times 10^2}{8 \times 10^{10}} \\[1em] = 3 \times 10^2 \times 10^{-10} = 3 \times 10^{2 + (-10)} \\[1em] = 3 \times 10^{-8}.⇒8×1010(4×107)(6×10−5)=8×10104×6×107×10−5=8×101024×107+(−5)=8×101024×102=3×102×10−10=3×102+(−10)=3×10−8.
Hence, (4×107)(6×10−5)8×1010=3×10−8.\dfrac{(4 \times 10^7)(6 \times 10^{-5})}{8 \times 10^{10}} = 3 \times 10^{-8}.8×1010(4×107)(6×10−5)=3×10−8.
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