Solve [(-4/5)^5*(-4/5)]^-1div(-4/5)^3

$$[ ( \frac { - 4 } { 5 } ) ^ { 5 } \times ( \frac { - 4 } { 5 } ) ] ^ { - 1 } \div ( - \frac { 4 } { 5 } ) ^ { 3 }$$

Evaluate

$$-\frac{1953125}{262144}=-7.450580597$$

Solution Steps

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

$$\frac{\left(\left(\frac{-4}{5}\right)^{6}\right)^{-1}}{\left(-\frac{4}{5}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and -1 to get -6.

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

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

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

Calculate -\frac{4}{5} to the power of -6 and get \frac{15625}{4096}.

$$\frac{\frac{15625}{4096}}{\left(-\frac{4}{5}\right)^{3}}$$

Calculate -\frac{4}{5} to the power of 3 and get -\frac{64}{125}.

$$\frac{\frac{15625}{4096}}{-\frac{64}{125}}$$

Divide \frac{15625}{4096} by -\frac{64}{125} by multiplying \frac{15625}{4096} by the reciprocal of -\frac{64}{125}.

$$\frac{15625}{4096}\left(-\frac{125}{64}\right)$$

Multiply \frac{15625}{4096} and -\frac{125}{64} to get -\frac{1953125}{262144}.

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

Factor

$$-\frac{1953125}{262144} = -7\frac{118117}{262144} = -7.450580596923828$$