Solve 2^{2}+5^{3}:5-2*3^{2}+(3^{2})^4:9^3+28-13-2^2*2^3

$$2 ^ { 2 } + 5 ^ { 3 } : 5 - 2 \times 3 ^ { 2 } + ( 3 ^ { 2 } ) ^ { 4 } : 9 ^ { 3 } + 28 - 13 - 2 ^ { 2 } \times 2 ^ { 3 }$$

Evaluate

$$3$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 1 from 3 to get 2.

$$2^{2}+5^{2}-2\times 3^{2}+\frac{\left(3^{2}\right)^{4}}{9^{3}}+28-13-2^{2}\times 2^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$2^{2}+5^{2}-2\times 3^{2}+\frac{3^{8}}{9^{3}}+28-13-2^{2}\times 2^{3}$$

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

$$2^{2}+5^{2}-2\times 3^{2}+\frac{3^{8}}{9^{3}}+28-13-2^{5}$$

Calculate 2 to the power of 2 and get 4.

$$4+5^{2}-2\times 3^{2}+\frac{3^{8}}{9^{3}}+28-13-2^{5}$$

Calculate 5 to the power of 2 and get 25.

$$4+25-2\times 3^{2}+\frac{3^{8}}{9^{3}}+28-13-2^{5}$$

Add 4 and 25 to get 29.

$$29-2\times 3^{2}+\frac{3^{8}}{9^{3}}+28-13-2^{5}$$

Calculate 3 to the power of 2 and get 9.

$$29-2\times 9+\frac{3^{8}}{9^{3}}+28-13-2^{5}$$

Multiply 2 and 9 to get 18.

$$29-18+\frac{3^{8}}{9^{3}}+28-13-2^{5}$$

Subtract 18 from 29 to get 11.

$$11+\frac{3^{8}}{9^{3}}+28-13-2^{5}$$

Calculate 3 to the power of 8 and get 6561.

$$11+\frac{6561}{9^{3}}+28-13-2^{5}$$

Calculate 9 to the power of 3 and get 729.

$$11+\frac{6561}{729}+28-13-2^{5}$$

Divide 6561 by 729 to get 9.

$$11+9+28-13-2^{5}$$

Add 11 and 9 to get 20.

$$20+28-13-2^{5}$$

Add 20 and 28 to get 48.

$$48-13-2^{5}$$

Subtract 13 from 48 to get 35.

$$35-2^{5}$$

Calculate 2 to the power of 5 and get 32.

$$35-32$$

Subtract 32 from 35 to get 3.

$$3$$

Factor

$$3$$