Solve [(-4/5)^5*(-4/5)]^2div(-4/5)^3)

$$[ ( \frac { - 4 } { 5 } ) ^ { 5 } \times ( \frac { - 4 } { 5 } ) ] ^ { 2 } \div ( \frac { - 4 } { 5 } ) ^ { 3 } )$$

Evaluate

$$-\frac{262144}{1953125}=-0.134217728$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$\frac{\left(\left(\frac{-4}{5}\right)^{6}\right)^{2}}{\left(\frac{-4}{5}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\frac{\left(\frac{-4}{5}\right)^{12}}{\left(\frac{-4}{5}\right)^{3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 12 to get 9.

$$\left(\frac{-4}{5}\right)^{9}$$

Fraction \frac{-4}{5} can be rewritten as -\frac{4}{5} by extracting the negative sign.

$$\left(-\frac{4}{5}\right)^{9}$$

Calculate -\frac{4}{5} to the power of 9 and get -\frac{262144}{1953125}.

$$-\frac{262144}{1953125}$$

Factor

$$-\frac{262144}{1953125} = -0.134217728$$