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

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

Evaluate

$$6$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$3+\frac{3\times \left(\frac{3^{12}}{3^{4}\times 3^{7}}\right)^{2}}{3^{2}}$$

To multiply powers of the same base, add their exponents. Add 4 and 7 to get 11.

$$3+\frac{3\times \left(\frac{3^{12}}{3^{11}}\right)^{2}}{3^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 11 from 12 to get 1.

$$3+\frac{3\times \left(3^{1}\right)^{2}}{3^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 1 and 2 to get 2.

$$3+\frac{3\times 3^{2}}{3^{2}}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

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

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

$$3+3^{1}$$

Calculate 3 to the power of 1 and get 3.

$$3+3$$

Add 3 and 3 to get 6.

$$6$$

Factor

$$2\times 3$$