Solve frac{35^{-1}*40^{-1}*10^2}{2^3*14^-1*5*20^2}=100

$$\frac { 35 ^ { - 1 } \cdot 40 ^ { - 1 } \cdot 10 ^ { 2 } } { 2 ^ { 3 } \cdot 14 ^ { - 1 } \cdot 5 \cdot 20 ^ { 2 } } = 100$$

Verify

Solution Steps

Calculate 35 to the power of -1 and get \frac{1}{35}.

$$\frac{\frac{1}{35}\times 40^{-1}\times 10^{2}}{2^{3}\times 14^{-1}\times 5\times 20^{2}}=100$$

Calculate 40 to the power of -1 and get \frac{1}{40}.

$$\frac{\frac{1}{35}\times \frac{1}{40}\times 10^{2}}{2^{3}\times 14^{-1}\times 5\times 20^{2}}=100$$

Multiply \frac{1}{35} and \frac{1}{40} to get \frac{1}{1400}.

$$\frac{\frac{1}{1400}\times 10^{2}}{2^{3}\times 14^{-1}\times 5\times 20^{2}}=100$$

Calculate 10 to the power of 2 and get 100.

$$\frac{\frac{1}{1400}\times 100}{2^{3}\times 14^{-1}\times 5\times 20^{2}}=100$$

Multiply \frac{1}{1400} and 100 to get \frac{1}{14}.

$$\frac{\frac{1}{14}}{2^{3}\times 14^{-1}\times 5\times 20^{2}}=100$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\frac{1}{14}}{8\times 14^{-1}\times 5\times 20^{2}}=100$$

Calculate 14 to the power of -1 and get \frac{1}{14}.

$$\frac{\frac{1}{14}}{8\times \frac{1}{14}\times 5\times 20^{2}}=100$$

Multiply 8 and \frac{1}{14} to get \frac{4}{7}.

$$\frac{\frac{1}{14}}{\frac{4}{7}\times 5\times 20^{2}}=100$$

Multiply \frac{4}{7} and 5 to get \frac{20}{7}.

$$\frac{\frac{1}{14}}{\frac{20}{7}\times 20^{2}}=100$$

Calculate 20 to the power of 2 and get 400.

$$\frac{\frac{1}{14}}{\frac{20}{7}\times 400}=100$$

Multiply \frac{20}{7} and 400 to get \frac{8000}{7}.

$$\frac{\frac{1}{14}}{\frac{8000}{7}}=100$$

Divide \frac{1}{14} by \frac{8000}{7} by multiplying \frac{1}{14} by the reciprocal of \frac{8000}{7}.

$$\frac{1}{14}\times \frac{7}{8000}=100$$

Multiply \frac{1}{14} and \frac{7}{8000} to get \frac{1}{16000}.

$$\frac{1}{16000}=100$$

Convert 100 to fraction \frac{1600000}{16000}.

$$\frac{1}{16000}=\frac{1600000}{16000}$$

Compare \frac{1}{16000} and \frac{1600000}{16000}.

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