Solve (-8/15)^7*(5/4)^7div(-2/3)^4

$$( - \frac { 8 } { 15 } ) ^ { 7 } \times ( \frac { 5 } { 4 } ) ^ { 7 } \div ( - \frac { 2 } { 3 } ) ^ { 4 }$$

Evaluate

$$-\frac{8}{27}\approx -0.296296296$$

Solution Steps

Calculate -\frac{8}{15} to the power of 7 and get -\frac{2097152}{170859375}.

$$\frac{-\frac{2097152}{170859375}\times \left(\frac{5}{4}\right)^{7}}{\left(-\frac{2}{3}\right)^{4}}$$

Calculate \frac{5}{4} to the power of 7 and get \frac{78125}{16384}.

$$\frac{-\frac{2097152}{170859375}\times \frac{78125}{16384}}{\left(-\frac{2}{3}\right)^{4}}$$

Multiply -\frac{2097152}{170859375} times \frac{78125}{16384} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{-2097152\times 78125}{170859375\times 16384}}{\left(-\frac{2}{3}\right)^{4}}$$

Do the multiplications in the fraction \frac{-2097152\times 78125}{170859375\times 16384}.

$$\frac{\frac{-163840000000}{2799360000000}}{\left(-\frac{2}{3}\right)^{4}}$$

Reduce the fraction \frac{-163840000000}{2799360000000} to lowest terms by extracting and canceling out 1280000000.

$$\frac{-\frac{128}{2187}}{\left(-\frac{2}{3}\right)^{4}}$$

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

$$\frac{-\frac{128}{2187}}{\frac{16}{81}}$$

Divide -\frac{128}{2187} by \frac{16}{81} by multiplying -\frac{128}{2187} by the reciprocal of \frac{16}{81}.

$$-\frac{128}{2187}\times \frac{81}{16}$$

Multiply -\frac{128}{2187} times \frac{81}{16} by multiplying numerator times numerator and denominator times denominator.

$$\frac{-128\times 81}{2187\times 16}$$

Do the multiplications in the fraction \frac{-128\times 81}{2187\times 16}.

$$\frac{-10368}{34992}$$

Reduce the fraction \frac{-10368}{34992} to lowest terms by extracting and canceling out 1296.

$$-\frac{8}{27}$$

Factor

$$-\frac{8}{27} = -0.2962962962962963$$