Solve (3-1/7)^-2/sqrt{10^4}=1

$$\frac { ( 3 - \frac { 1 } { 7 } ) ^ { - 2 } } { \sqrt { 10 ^ { 4 } } } = 1$$

Verify

Solution Steps

Subtract \frac{1}{7} from 3 to get \frac{20}{7}.

$$\frac{\left(\frac{20}{7}\right)^{-2}}{\sqrt{10^{4}}}=1$$

Calculate \frac{20}{7} to the power of -2 and get \frac{49}{400}.

$$\frac{\frac{49}{400}}{\sqrt{10^{4}}}=1$$

Calculate 10 to the power of 4 and get 10000.

$$\frac{\frac{49}{400}}{\sqrt{10000}}=1$$

Calculate the square root of 10000 and get 100.

$$\frac{\frac{49}{400}}{100}=1$$

Express \frac{\frac{49}{400}}{100} as a single fraction.

$$\frac{49}{400\times 100}=1$$

Multiply 400 and 100 to get 40000.

$$\frac{49}{40000}=1$$

Convert 1 to fraction \frac{40000}{40000}.

$$\frac{49}{40000}=\frac{40000}{40000}$$

Compare \frac{49}{40000} and \frac{40000}{40000}.

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