Solve (2/3)^4(-3/5)^3+(4/7div5/9)^2

$$( \frac { 2 } { 3 } ) ^ { 4 } ( \frac { - 3 } { 5 } ) ^ { 3 } + ( \frac { 4 } { 7 } \div \frac { 5 } { 9 } ) ^ { 2 }$$

Evaluate

$$\frac{18656}{18375}\approx 1.015292517$$

Solution Steps

Calculate \frac{2}{3} to the power of 4 and get \frac{16}{81}.

$$\frac{16}{81}\times \left(\frac{-3}{5}\right)^{3}+\left(\frac{\frac{4}{7}}{\frac{5}{9}}\right)^{2}$$

Fraction \frac{-3}{5} can be rewritten as -\frac{3}{5} by extracting the negative sign.

$$\frac{16}{81}\left(-\frac{3}{5}\right)^{3}+\left(\frac{\frac{4}{7}}{\frac{5}{9}}\right)^{2}$$

Calculate -\frac{3}{5} to the power of 3 and get -\frac{27}{125}.

$$\frac{16}{81}\left(-\frac{27}{125}\right)+\left(\frac{\frac{4}{7}}{\frac{5}{9}}\right)^{2}$$

Multiply \frac{16}{81} and -\frac{27}{125} to get -\frac{16}{375}.

$$-\frac{16}{375}+\left(\frac{\frac{4}{7}}{\frac{5}{9}}\right)^{2}$$

Divide \frac{4}{7} by \frac{5}{9} by multiplying \frac{4}{7} by the reciprocal of \frac{5}{9}.

$$-\frac{16}{375}+\left(\frac{4}{7}\times \frac{9}{5}\right)^{2}$$

Multiply \frac{4}{7} and \frac{9}{5} to get \frac{36}{35}.

$$-\frac{16}{375}+\left(\frac{36}{35}\right)^{2}$$

Calculate \frac{36}{35} to the power of 2 and get \frac{1296}{1225}.

$$-\frac{16}{375}+\frac{1296}{1225}$$

Add -\frac{16}{375} and \frac{1296}{1225} to get \frac{18656}{18375}.

$$\frac{18656}{18375}$$

Factor

$$\frac{2 ^ {5} \cdot 11 \cdot 53}{3 \cdot 5 ^ {3} \cdot 7 ^ {2}} = 1\frac{281}{18375} = 1.0152925170068028$$