Solve -3/4{left(2/5right)}^-5

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

Evaluate

$$-\frac{53}{10}=-5.3$$

Solution Steps

Fraction \frac{-3}{4} can be rewritten as -\frac{3}{4} by extracting the negative sign.

$$-\frac{3}{4}\times \left(\frac{2}{5}\right)^{1}-5$$

Calculate \frac{2}{5} to the power of 1 and get \frac{2}{5}.

$$-\frac{3}{4}\times \frac{2}{5}-5$$

Multiply -\frac{3}{4} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-3\times 2}{4\times 5}-5$$

Do the multiplications in the fraction \frac{-3\times 2}{4\times 5}.

$$\frac{-6}{20}-5$$

Reduce the fraction \frac{-6}{20} to lowest terms by extracting and canceling out 2.

$$-\frac{3}{10}-5$$

Convert 5 to fraction \frac{50}{10}.

$$-\frac{3}{10}-\frac{50}{10}$$

Since -\frac{3}{10} and \frac{50}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{-3-50}{10}$$

Subtract 50 from -3 to get -53.

$$-\frac{53}{10}$$

Factor

$$-\frac{53}{10} = -5\frac{3}{10} = -5.3$$