Solve (-36/25)^4*(-5/24)^4:(27/100)^4

$$( - \frac { 36 } { 25 } ) ^ { 4 } \cdot ( - \frac { 5 } { 24 } ) ^ { 4 } : ( \frac { 27 } { 100 } ) ^ { 4 }$$

Evaluate

$$\frac{10000}{6561}\approx 1.524157903$$

Solution Steps

Calculate -\frac{36}{25} to the power of 4 and get \frac{1679616}{390625}.

$$\frac{\frac{1679616}{390625}\left(-\frac{5}{24}\right)^{4}}{\left(\frac{27}{100}\right)^{4}}$$

Calculate -\frac{5}{24} to the power of 4 and get \frac{625}{331776}.

$$\frac{\frac{1679616}{390625}\times \frac{625}{331776}}{\left(\frac{27}{100}\right)^{4}}$$

Multiply \frac{1679616}{390625} times \frac{625}{331776} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1679616\times 625}{390625\times 331776}}{\left(\frac{27}{100}\right)^{4}}$$

Do the multiplications in the fraction \frac{1679616\times 625}{390625\times 331776}.

$$\frac{\frac{1049760000}{129600000000}}{\left(\frac{27}{100}\right)^{4}}$$

Reduce the fraction \frac{1049760000}{129600000000} to lowest terms by extracting and canceling out 12960000.

$$\frac{\frac{81}{10000}}{\left(\frac{27}{100}\right)^{4}}$$

Calculate \frac{27}{100} to the power of 4 and get \frac{531441}{100000000}.

$$\frac{\frac{81}{10000}}{\frac{531441}{100000000}}$$

Divide \frac{81}{10000} by \frac{531441}{100000000} by multiplying \frac{81}{10000} by the reciprocal of \frac{531441}{100000000}.

$$\frac{81}{10000}\times \frac{100000000}{531441}$$

Multiply \frac{81}{10000} times \frac{100000000}{531441} by multiplying numerator times numerator and denominator times denominator.

$$\frac{81\times 100000000}{10000\times 531441}$$

Do the multiplications in the fraction \frac{81\times 100000000}{10000\times 531441}.

$$\frac{8100000000}{5314410000}$$

Reduce the fraction \frac{8100000000}{5314410000} to lowest terms by extracting and canceling out 810000.

$$\frac{10000}{6561}$$

Factor

$$\frac{2 ^ {4} \cdot 5 ^ {4}}{3 ^ {8}} = 1\frac{3439}{6561} = 1.5241579027587258$$