Solve 3*4^3+16*4+4^5*1/5-3/24^4+12*16-8/3*4^3=

$$3 \times { 4 }^{ 3 } +16 \times 4+ { 4 }^{ 5 } \times \frac{ 1 }{ 5 } - \frac{ 3 }{ 2 } { 4 }^{ 4 } +12 \times 16- \frac{ 8 }{ 3 } \times { 4 }^{ 3 } =$$

Evaluate

$$\frac{1472}{15}\approx 98.133333333$$

Solution Steps

Calculate 4 to the power of 3 and get 64.

$$3\times 64+16\times 4+4^{5}\times \frac{1}{5}-\frac{3}{2}\times 4^{4}+12\times 16-\frac{8}{3}\times 4^{3}$$

Multiply 3 and 64 to get 192.

$$192+16\times 4+4^{5}\times \frac{1}{5}-\frac{3}{2}\times 4^{4}+12\times 16-\frac{8}{3}\times 4^{3}$$

Multiply 16 and 4 to get 64.

$$192+64+4^{5}\times \frac{1}{5}-\frac{3}{2}\times 4^{4}+12\times 16-\frac{8}{3}\times 4^{3}$$

Add 192 and 64 to get 256.

$$256+4^{5}\times \frac{1}{5}-\frac{3}{2}\times 4^{4}+12\times 16-\frac{8}{3}\times 4^{3}$$

Calculate 4 to the power of 5 and get 1024.

$$256+1024\times \frac{1}{5}-\frac{3}{2}\times 4^{4}+12\times 16-\frac{8}{3}\times 4^{3}$$

Multiply 1024 and \frac{1}{5} to get \frac{1024}{5}.

$$256+\frac{1024}{5}-\frac{3}{2}\times 4^{4}+12\times 16-\frac{8}{3}\times 4^{3}$$

Convert 256 to fraction \frac{1280}{5}.

$$\frac{1280}{5}+\frac{1024}{5}-\frac{3}{2}\times 4^{4}+12\times 16-\frac{8}{3}\times 4^{3}$$

Since \frac{1280}{5} and \frac{1024}{5} have the same denominator, add them by adding their numerators.

$$\frac{1280+1024}{5}-\frac{3}{2}\times 4^{4}+12\times 16-\frac{8}{3}\times 4^{3}$$

Add 1280 and 1024 to get 2304.

$$\frac{2304}{5}-\frac{3}{2}\times 4^{4}+12\times 16-\frac{8}{3}\times 4^{3}$$

Calculate 4 to the power of 4 and get 256.

$$\frac{2304}{5}-\frac{3}{2}\times 256+12\times 16-\frac{8}{3}\times 4^{3}$$

Express \frac{3}{2}\times 256 as a single fraction.

$$\frac{2304}{5}-\frac{3\times 256}{2}+12\times 16-\frac{8}{3}\times 4^{3}$$

Multiply 3 and 256 to get 768.

$$\frac{2304}{5}-\frac{768}{2}+12\times 16-\frac{8}{3}\times 4^{3}$$

Divide 768 by 2 to get 384.

$$\frac{2304}{5}-384+12\times 16-\frac{8}{3}\times 4^{3}$$

Convert 384 to fraction \frac{1920}{5}.

$$\frac{2304}{5}-\frac{1920}{5}+12\times 16-\frac{8}{3}\times 4^{3}$$

Since \frac{2304}{5} and \frac{1920}{5} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2304-1920}{5}+12\times 16-\frac{8}{3}\times 4^{3}$$

Subtract 1920 from 2304 to get 384.

$$\frac{384}{5}+12\times 16-\frac{8}{3}\times 4^{3}$$

Multiply 12 and 16 to get 192.

$$\frac{384}{5}+192-\frac{8}{3}\times 4^{3}$$

Convert 192 to fraction \frac{960}{5}.

$$\frac{384}{5}+\frac{960}{5}-\frac{8}{3}\times 4^{3}$$

Since \frac{384}{5} and \frac{960}{5} have the same denominator, add them by adding their numerators.

$$\frac{384+960}{5}-\frac{8}{3}\times 4^{3}$$

Add 384 and 960 to get 1344.

$$\frac{1344}{5}-\frac{8}{3}\times 4^{3}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{1344}{5}-\frac{8}{3}\times 64$$

Express \frac{8}{3}\times 64 as a single fraction.

$$\frac{1344}{5}-\frac{8\times 64}{3}$$

Multiply 8 and 64 to get 512.

$$\frac{1344}{5}-\frac{512}{3}$$

Least common multiple of 5 and 3 is 15. Convert \frac{1344}{5} and \frac{512}{3} to fractions with denominator 15.

$$\frac{4032}{15}-\frac{2560}{15}$$

Since \frac{4032}{15} and \frac{2560}{15} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4032-2560}{15}$$

Subtract 2560 from 4032 to get 1472.

$$\frac{1472}{15}$$

Factor

$$\frac{2 ^ {6} \cdot 23}{3 \cdot 5} = 98\frac{2}{15} = 98.13333333333334$$