Solve 2^{4}(12^2div3*4)-3(2^3*2)+5^2(150-12^2)

$$2 ^ { 4 } ( 12 ^ { 2 } \div 3 \cdot 4 ) - 3 ( 2 ^ { 3 } \cdot 2 ) + 5 ^ { 2 } ( 150 - 12 ^ { 2 } )$$

Evaluate

$$3174$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$2^{4}\times \frac{12^{2}}{3}\times 4-3\times 2^{4}+5^{2}\left(150-12^{2}\right)$$

Calculate 2 to the power of 4 and get 16.

$$16\times \frac{12^{2}}{3}\times 4-3\times 2^{4}+5^{2}\left(150-12^{2}\right)$$

Calculate 12 to the power of 2 and get 144.

$$16\times \frac{144}{3}\times 4-3\times 2^{4}+5^{2}\left(150-12^{2}\right)$$

Divide 144 by 3 to get 48.

$$16\times 48\times 4-3\times 2^{4}+5^{2}\left(150-12^{2}\right)$$

Multiply 16 and 48 to get 768.

$$768\times 4-3\times 2^{4}+5^{2}\left(150-12^{2}\right)$$

Multiply 768 and 4 to get 3072.

$$3072-3\times 2^{4}+5^{2}\left(150-12^{2}\right)$$

Calculate 2 to the power of 4 and get 16.

$$3072-3\times 16+5^{2}\left(150-12^{2}\right)$$

Multiply 3 and 16 to get 48.

$$3072-48+5^{2}\left(150-12^{2}\right)$$

Subtract 48 from 3072 to get 3024.

$$3024+5^{2}\left(150-12^{2}\right)$$

Calculate 5 to the power of 2 and get 25.

$$3024+25\left(150-12^{2}\right)$$

Calculate 12 to the power of 2 and get 144.

$$3024+25\left(150-144\right)$$

Subtract 144 from 150 to get 6.

$$3024+25\times 6$$

Multiply 25 and 6 to get 150.

$$3024+150$$

Add 3024 and 150 to get 3174.

$$3174$$

Factor

$$2\times 3\times 23^{2}$$