Solve (1-0,4^4*315/25:9/55-6:17/13))

$$( 1 - 0,4 ^ { 4 } \cdot 3 \frac { 15 } { 25 } : \frac { 9 } { 55 } - 6 : 1 \frac { 7 } { 13 } ) )$$

Evaluate

$$-3.4632$$

Solution Steps

Calculate 0.4 to the power of 4 and get 0.0256.

$$1-\frac{0.0256\times \frac{3\times 25+15}{25}}{\frac{9}{55}}-\frac{6}{\frac{1\times 13+7}{13}}$$

Multiply 3 and 25 to get 75.

$$1-\frac{0.0256\times \frac{75+15}{25}}{\frac{9}{55}}-\frac{6}{\frac{1\times 13+7}{13}}$$

Add 75 and 15 to get 90.

$$1-\frac{0.0256\times \frac{90}{25}}{\frac{9}{55}}-\frac{6}{\frac{1\times 13+7}{13}}$$

Reduce the fraction \frac{90}{25} to lowest terms by extracting and canceling out 5.

$$1-\frac{0.0256\times \frac{18}{5}}{\frac{9}{55}}-\frac{6}{\frac{1\times 13+7}{13}}$$

Convert decimal number 0.0256 to fraction \frac{256}{10000}. Reduce the fraction \frac{256}{10000} to lowest terms by extracting and canceling out 16.

$$1-\frac{\frac{16}{625}\times \frac{18}{5}}{\frac{9}{55}}-\frac{6}{\frac{1\times 13+7}{13}}$$

Multiply \frac{16}{625} times \frac{18}{5} by multiplying numerator times numerator and denominator times denominator.

$$1-\frac{\frac{16\times 18}{625\times 5}}{\frac{9}{55}}-\frac{6}{\frac{1\times 13+7}{13}}$$

Do the multiplications in the fraction \frac{16\times 18}{625\times 5}.

$$1-\frac{\frac{288}{3125}}{\frac{9}{55}}-\frac{6}{\frac{1\times 13+7}{13}}$$

Divide \frac{288}{3125} by \frac{9}{55} by multiplying \frac{288}{3125} by the reciprocal of \frac{9}{55}.

$$1-\frac{288}{3125}\times \frac{55}{9}-\frac{6}{\frac{1\times 13+7}{13}}$$

Multiply \frac{288}{3125} times \frac{55}{9} by multiplying numerator times numerator and denominator times denominator.

$$1-\frac{288\times 55}{3125\times 9}-\frac{6}{\frac{1\times 13+7}{13}}$$

Do the multiplications in the fraction \frac{288\times 55}{3125\times 9}.

$$1-\frac{15840}{28125}-\frac{6}{\frac{1\times 13+7}{13}}$$

Reduce the fraction \frac{15840}{28125} to lowest terms by extracting and canceling out 45.

$$1-\frac{352}{625}-\frac{6}{\frac{1\times 13+7}{13}}$$

Convert 1 to fraction \frac{625}{625}.

$$\frac{625}{625}-\frac{352}{625}-\frac{6}{\frac{1\times 13+7}{13}}$$

Since \frac{625}{625} and \frac{352}{625} have the same denominator, subtract them by subtracting their numerators.

$$\frac{625-352}{625}-\frac{6}{\frac{1\times 13+7}{13}}$$

Subtract 352 from 625 to get 273.

$$\frac{273}{625}-\frac{6}{\frac{1\times 13+7}{13}}$$

Divide 6 by \frac{1\times 13+7}{13} by multiplying 6 by the reciprocal of \frac{1\times 13+7}{13}.

$$\frac{273}{625}-\frac{6\times 13}{1\times 13+7}$$

Multiply 6 and 13 to get 78.

$$\frac{273}{625}-\frac{78}{1\times 13+7}$$

Multiply 1 and 13 to get 13.

$$\frac{273}{625}-\frac{78}{13+7}$$

Add 13 and 7 to get 20.

$$\frac{273}{625}-\frac{78}{20}$$

Reduce the fraction \frac{78}{20} to lowest terms by extracting and canceling out 2.

$$\frac{273}{625}-\frac{39}{10}$$

Least common multiple of 625 and 10 is 1250. Convert \frac{273}{625} and \frac{39}{10} to fractions with denominator 1250.

$$\frac{546}{1250}-\frac{4875}{1250}$$

Since \frac{546}{1250} and \frac{4875}{1250} have the same denominator, subtract them by subtracting their numerators.

$$\frac{546-4875}{1250}$$

Subtract 4875 from 546 to get -4329.

$$-\frac{4329}{1250}$$

Factor

$$-3.4632$$