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

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

Evaluate

$$7$$

Solution Steps

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

$$\frac{3^{4}-3^{2}}{2^{3}}-\frac{3^{5}}{3^{4}}+5^{0}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 5 to get 1.

$$\frac{3^{4}-3^{2}}{2^{3}}-3^{1}+5^{0}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{81-3^{2}}{2^{3}}-3^{1}+5^{0}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{81-9}{2^{3}}-3^{1}+5^{0}$$

Subtract 9 from 81 to get 72.

$$\frac{72}{2^{3}}-3^{1}+5^{0}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{72}{8}-3^{1}+5^{0}$$

Divide 72 by 8 to get 9.

$$9-3^{1}+5^{0}$$

Calculate 3 to the power of 1 and get 3.

$$9-3+5^{0}$$

Subtract 3 from 9 to get 6.

$$6+5^{0}$$

Calculate 5 to the power of 0 and get 1.

$$6+1$$

Add 6 and 1 to get 7.

$$7$$

Factor

$$7$$