Solve [3*5*5^{0}-(2^{2}*2^{3}:4^2)^2+(8^4)^0]:3

$$[ 3 \cdot 5 \cdot 5 ^ { 0 } - ( 2 ^ { 2 } \cdot 2 ^ { 3 } : 4 ^ { 2 } ) ^ { 2 } + ( 8 ^ { 4 } ) ^ { 0 } ] : 3$$

Evaluate

$$4$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 0 to get 1.

$$\frac{3\times 5^{1}-\left(\frac{2^{2}\times 2^{3}}{4^{2}}\right)^{2}+\left(8^{4}\right)^{0}}{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{3\times 5^{1}-\left(\frac{2^{5}}{4^{2}}\right)^{2}+\left(8^{4}\right)^{0}}{3}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 0 to get 0.

$$\frac{3\times 5^{1}-\left(\frac{2^{5}}{4^{2}}\right)^{2}+8^{0}}{3}$$

Calculate 5 to the power of 1 and get 5.

$$\frac{3\times 5-\left(\frac{2^{5}}{4^{2}}\right)^{2}+8^{0}}{3}$$

Multiply 3 and 5 to get 15.

$$\frac{15-\left(\frac{2^{5}}{4^{2}}\right)^{2}+8^{0}}{3}$$

Calculate 2 to the power of 5 and get 32.

$$\frac{15-\left(\frac{32}{4^{2}}\right)^{2}+8^{0}}{3}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{15-\left(\frac{32}{16}\right)^{2}+8^{0}}{3}$$

Divide 32 by 16 to get 2.

$$\frac{15-2^{2}+8^{0}}{3}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{15-4+8^{0}}{3}$$

Subtract 4 from 15 to get 11.

$$\frac{11+8^{0}}{3}$$

Calculate 8 to the power of 0 and get 1.

$$\frac{11+1}{3}$$

Add 11 and 1 to get 12.

$$\frac{12}{3}$$

Divide 12 by 3 to get 4.

$$4$$

Factor

$$2^{2}$$