If 10m=210^{m}=2 and 10n=310^{n}=3, find the value of 103m−n10^{3m-n}. Answer ...

Laws of indicesNumber systems中文
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Worked solution

3

1. Rewrite the expression using laws of indices

103m−n=103m10n=(10m)310n10^{3m-n}=\frac{10^{3m}}{10^n}=\frac{(10^m)^3}{10^n}

2. Substitute the given values and evaluate

Given 10m=210^m=2 and 10n=310^n=3,
103m−n=(10m)310n=233=8310^{3m-n}=\frac{(10^m)^3}{10^n}=\frac{2^3}{3}=\frac{8}{3}

Answer

83\dfrac{8}{3}

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