Solve [7+(5^{2})^3:5^4]:2^4+3^3

$$[ 7 + ( 5 ^ { 2 } ) ^ { 3 } : 5 ^ { 4 } ] : 2 ^ { 4 } + 3 ^ { 3 }$$

Evaluate

$$29$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{7+\frac{5^{6}}{5^{4}}}{2^{4}}+3^{3}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 6 to get 2.

$$\frac{7+5^{2}}{2^{4}}+3^{3}$$

Calculate 5 to the power of 2 and get 25.

$$\frac{7+25}{2^{4}}+3^{3}$$

Add 7 and 25 to get 32.

$$\frac{32}{2^{4}}+3^{3}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{32}{16}+3^{3}$$

Divide 32 by 16 to get 2.

$$2+3^{3}$$

Calculate 3 to the power of 3 and get 27.

$$2+27$$

Add 2 and 27 to get 29.

$$29$$

Factor

$$29$$