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

Basic Math

Pre-Algebra

Algebra

Trigonometry

Calculus

Precalculus

Statistics

Finite Math

Linear Algebra

Chemistry

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

$\frac{64}{15625}=0.004096$

Solution Steps

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

$$\frac{\left(\frac{2}{5}\right)^{8}}{\left(\frac{2}{5}\right)^{2}}$$

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

$$\left(\frac{2}{5}\right)^{6}$$

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

$$\frac{64}{15625}$$

Show Solution

Factor

$\frac{2 ^ {6}}{5 ^ {6}} = 0.004096$