Solve [(\{(2/5) ^ 4\} ^ 2) / ((2/5) ^ 2)] * (1/2) ^ - 2 * (2) ^ - 1 * (1/4) ^ - 1

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Question

$$[\{(\frac{2}{5})^{4}\}^{2}\div(\frac{2}{5})^{2}]\times(\frac{1}{2})^{-2}\times(2)^{-1}\times(\frac{1}{4})^{-1}$$

Evaluate

$\frac{512}{15625}=0.032768$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply $4$ and $2$ to get $8$.

$$\frac{\left(\frac{2}{5}\right)^{8}}{\left(\frac{2}{5}\right)^{2}}\times \left(\frac{1}{2}\right)^{-2}\times 2^{-1}\times \left(\frac{1}{4}\right)^{-1}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract $2$ from $8$ to get $6$.

$$\left(\frac{2}{5}\right)^{6}\times \left(\frac{1}{2}\right)^{-2}\times 2^{-1}\times \left(\frac{1}{4}\right)^{-1}$$

Calculate $\frac{2}{5}$ to the power of $6$ and get $\frac{64}{15625}$.

$$\frac{64}{15625}\times \left(\frac{1}{2}\right)^{-2}\times 2^{-1}\times \left(\frac{1}{4}\right)^{-1}$$

Calculate $\frac{1}{2}$ to the power of $-2$ and get $4$.

$$\frac{64}{15625}\times 4\times 2^{-1}\times \left(\frac{1}{4}\right)^{-1}$$

Multiply $\frac{64}{15625}$ and $4$ to get $\frac{256}{15625}$.

$$\frac{256}{15625}\times 2^{-1}\times \left(\frac{1}{4}\right)^{-1}$$

Calculate $2$ to the power of $-1$ and get $\frac{1}{2}$.

$$\frac{256}{15625}\times \frac{1}{2}\times \left(\frac{1}{4}\right)^{-1}$$

Multiply $\frac{256}{15625}$ and $\frac{1}{2}$ to get $\frac{128}{15625}$.

$$\frac{128}{15625}\times \left(\frac{1}{4}\right)^{-1}$$

Calculate $\frac{1}{4}$ to the power of $-1$ and get $4$.

$$\frac{128}{15625}\times 4$$

Multiply $\frac{128}{15625}$ and $4$ to get $\frac{512}{15625}$.

$$\frac{512}{15625}$$

Show Solution

Factor

$\frac{2 ^ {9}}{5 ^ {6}} = 0.032768$