Solve (-5)^3*(-1/5)^2quadtext{(ii)}(15/16)^3div(9/8)^2

$$( - 5 ) ^ { 3 } \times ( - \frac { 1 } { 5 } ) ^ { 2 } \quad \text { (ii) } ( \frac { 15 } { 16 } ) ^ { 3 } \div ( \frac { 9 } { 8 } ) ^ { 2 }$$

Evaluate

$$\frac{625}{192}\approx 3.255208333$$

Solution Steps

Calculate -5 to the power of 3 and get -125.

$$\frac{-125\left(-\frac{1}{5}\right)^{2}ii\times \left(\frac{15}{16}\right)^{3}}{\left(\frac{9}{8}\right)^{2}}$$

Calculate -\frac{1}{5} to the power of 2 and get \frac{1}{25}.

$$\frac{-125\times \left(\frac{1}{25}i\right)i\times \left(\frac{15}{16}\right)^{3}}{\left(\frac{9}{8}\right)^{2}}$$

Multiply -125 and \frac{1}{25}i to get -5i.

$$\frac{-5ii\times \left(\frac{15}{16}\right)^{3}}{\left(\frac{9}{8}\right)^{2}}$$

Multiply -5i and i to get 5.

$$\frac{5\times \left(\frac{15}{16}\right)^{3}}{\left(\frac{9}{8}\right)^{2}}$$

Calculate \frac{15}{16} to the power of 3 and get \frac{3375}{4096}.

$$\frac{5\times \frac{3375}{4096}}{\left(\frac{9}{8}\right)^{2}}$$

Express 5\times \frac{3375}{4096} as a single fraction.

$$\frac{\frac{5\times 3375}{4096}}{\left(\frac{9}{8}\right)^{2}}$$

Multiply 5 and 3375 to get 16875.

$$\frac{\frac{16875}{4096}}{\left(\frac{9}{8}\right)^{2}}$$

Calculate \frac{9}{8} to the power of 2 and get \frac{81}{64}.

$$\frac{\frac{16875}{4096}}{\frac{81}{64}}$$

Divide \frac{16875}{4096} by \frac{81}{64} by multiplying \frac{16875}{4096} by the reciprocal of \frac{81}{64}.

$$\frac{16875}{4096}\times \frac{64}{81}$$

Multiply \frac{16875}{4096} times \frac{64}{81} by multiplying numerator times numerator and denominator times denominator.

$$\frac{16875\times 64}{4096\times 81}$$

Do the multiplications in the fraction \frac{16875\times 64}{4096\times 81}.

$$\frac{1080000}{331776}$$

Reduce the fraction \frac{1080000}{331776} to lowest terms by extracting and canceling out 1728.

$$\frac{625}{192}$$

Real Part

$$\frac{625}{192} = 3\frac{49}{192} = 3.2552083333333335$$

Solution Steps

Calculate -5 to the power of 3 and get -125.

$$Re(\frac{-125\left(-\frac{1}{5}\right)^{2}ii\times \left(\frac{15}{16}\right)^{3}}{\left(\frac{9}{8}\right)^{2}})$$

Calculate -\frac{1}{5} to the power of 2 and get \frac{1}{25}.

$$Re(\frac{-125\times \left(\frac{1}{25}i\right)i\times \left(\frac{15}{16}\right)^{3}}{\left(\frac{9}{8}\right)^{2}})$$

Multiply -125 and \frac{1}{25}i to get -5i.

$$Re(\frac{-5ii\times \left(\frac{15}{16}\right)^{3}}{\left(\frac{9}{8}\right)^{2}})$$

Multiply -5i and i to get 5.

$$Re(\frac{5\times \left(\frac{15}{16}\right)^{3}}{\left(\frac{9}{8}\right)^{2}})$$

Calculate \frac{15}{16} to the power of 3 and get \frac{3375}{4096}.

$$Re(\frac{5\times \frac{3375}{4096}}{\left(\frac{9}{8}\right)^{2}})$$

Express 5\times \frac{3375}{4096} as a single fraction.

$$Re(\frac{\frac{5\times 3375}{4096}}{\left(\frac{9}{8}\right)^{2}})$$

Multiply 5 and 3375 to get 16875.

$$Re(\frac{\frac{16875}{4096}}{\left(\frac{9}{8}\right)^{2}})$$

Calculate \frac{9}{8} to the power of 2 and get \frac{81}{64}.

$$Re(\frac{\frac{16875}{4096}}{\frac{81}{64}})$$

Divide \frac{16875}{4096} by \frac{81}{64} by multiplying \frac{16875}{4096} by the reciprocal of \frac{81}{64}.

$$Re(\frac{16875}{4096}\times \frac{64}{81})$$

Multiply \frac{16875}{4096} times \frac{64}{81} by multiplying numerator times numerator and denominator times denominator.

$$Re(\frac{16875\times 64}{4096\times 81})$$

Do the multiplications in the fraction \frac{16875\times 64}{4096\times 81}.

$$Re(\frac{1080000}{331776})$$

Reduce the fraction \frac{1080000}{331776} to lowest terms by extracting and canceling out 1728.

$$Re(\frac{625}{192})$$

The real part of \frac{625}{192} is \frac{625}{192}.

$$\frac{625}{192}$$