Solve [-24^4-(-2)^3+(-24)^4]*[-2/3+17/8*(-1/4)*4.5-6^2]+32

$$[ - 24 ^ { 4 } - ( - 2 ) ^ { 3 } + ( - 24 ) ^ { 4 } ] \times [ - \frac { 2 } { 3 } + 1 \frac { 7 } { 8 } \times ( - \frac { 1 } { 4 } ) \times 4.5 - 6 ^ { 2 } ] + 32$$

Evaluate

$$-\frac{6677}{24}\approx -278.208333333$$

Solution Steps

Calculate 24 to the power of 4 and get 331776.

$$\left(-331776-\left(-2\right)^{3}+\left(-24\right)^{4}\right)\left(-\frac{2}{3}+\frac{1\times 8+7}{8}\left(-\frac{1}{4}\right)\times 4.5-6^{2}\right)+32$$

Calculate -2 to the power of 3 and get -8.

$$\left(-331776-\left(-8\right)+\left(-24\right)^{4}\right)\left(-\frac{2}{3}+\frac{1\times 8+7}{8}\left(-\frac{1}{4}\right)\times 4.5-6^{2}\right)+32$$

The opposite of -8 is 8.

$$\left(-331776+8+\left(-24\right)^{4}\right)\left(-\frac{2}{3}+\frac{1\times 8+7}{8}\left(-\frac{1}{4}\right)\times 4.5-6^{2}\right)+32$$

Add -331776 and 8 to get -331768.

$$\left(-331768+\left(-24\right)^{4}\right)\left(-\frac{2}{3}+\frac{1\times 8+7}{8}\left(-\frac{1}{4}\right)\times 4.5-6^{2}\right)+32$$

Calculate -24 to the power of 4 and get 331776.

$$\left(-331768+331776\right)\left(-\frac{2}{3}+\frac{1\times 8+7}{8}\left(-\frac{1}{4}\right)\times 4.5-6^{2}\right)+32$$

Add -331768 and 331776 to get 8.

$$8\left(-\frac{2}{3}+\frac{1\times 8+7}{8}\left(-\frac{1}{4}\right)\times 4.5-6^{2}\right)+32$$

Multiply 1 and 8 to get 8.

$$8\left(-\frac{2}{3}+\frac{8+7}{8}\left(-\frac{1}{4}\right)\times 4.5-6^{2}\right)+32$$

Add 8 and 7 to get 15.

$$8\left(-\frac{2}{3}+\frac{15}{8}\left(-\frac{1}{4}\right)\times 4.5-6^{2}\right)+32$$

Multiply \frac{15}{8} times -\frac{1}{4} by multiplying numerator times numerator and denominator times denominator.

$$8\left(-\frac{2}{3}+\frac{15\left(-1\right)}{8\times 4}\times 4.5-6^{2}\right)+32$$

Do the multiplications in the fraction \frac{15\left(-1\right)}{8\times 4}.

$$8\left(-\frac{2}{3}+\frac{-15}{32}\times 4.5-6^{2}\right)+32$$

Fraction \frac{-15}{32} can be rewritten as -\frac{15}{32} by extracting the negative sign.

$$8\left(-\frac{2}{3}-\frac{15}{32}\times 4.5-6^{2}\right)+32$$

Convert decimal number 4.5 to fraction \frac{45}{10}. Reduce the fraction \frac{45}{10} to lowest terms by extracting and canceling out 5.

$$8\left(-\frac{2}{3}-\frac{15}{32}\times \frac{9}{2}-6^{2}\right)+32$$

Multiply -\frac{15}{32} times \frac{9}{2} by multiplying numerator times numerator and denominator times denominator.

$$8\left(-\frac{2}{3}+\frac{-15\times 9}{32\times 2}-6^{2}\right)+32$$

Do the multiplications in the fraction \frac{-15\times 9}{32\times 2}.

$$8\left(-\frac{2}{3}+\frac{-135}{64}-6^{2}\right)+32$$

Fraction \frac{-135}{64} can be rewritten as -\frac{135}{64} by extracting the negative sign.

$$8\left(-\frac{2}{3}-\frac{135}{64}-6^{2}\right)+32$$

Least common multiple of 3 and 64 is 192. Convert -\frac{2}{3} and \frac{135}{64} to fractions with denominator 192.

$$8\left(-\frac{128}{192}-\frac{405}{192}-6^{2}\right)+32$$

Since -\frac{128}{192} and \frac{405}{192} have the same denominator, subtract them by subtracting their numerators.

$$8\left(\frac{-128-405}{192}-6^{2}\right)+32$$

Subtract 405 from -128 to get -533.

$$8\left(-\frac{533}{192}-6^{2}\right)+32$$

Calculate 6 to the power of 2 and get 36.

$$8\left(-\frac{533}{192}-36\right)+32$$

Convert 36 to fraction \frac{6912}{192}.

$$8\left(-\frac{533}{192}-\frac{6912}{192}\right)+32$$

Since -\frac{533}{192} and \frac{6912}{192} have the same denominator, subtract them by subtracting their numerators.

$$8\times \frac{-533-6912}{192}+32$$

Subtract 6912 from -533 to get -7445.

$$8\left(-\frac{7445}{192}\right)+32$$

Express 8\left(-\frac{7445}{192}\right) as a single fraction.

$$\frac{8\left(-7445\right)}{192}+32$$

Multiply 8 and -7445 to get -59560.

$$\frac{-59560}{192}+32$$

Reduce the fraction \frac{-59560}{192} to lowest terms by extracting and canceling out 8.

$$-\frac{7445}{24}+32$$

Convert 32 to fraction \frac{768}{24}.

$$-\frac{7445}{24}+\frac{768}{24}$$

Since -\frac{7445}{24} and \frac{768}{24} have the same denominator, add them by adding their numerators.

$$\frac{-7445+768}{24}$$

Add -7445 and 768 to get -6677.

$$-\frac{6677}{24}$$

Factor

$$-\frac{6677}{24} = -278\frac{5}{24} = -278.2083333333333$$