Solve [(3^{4}*3^{7}*3^{5})^{2}:3^{30}]^2:(3^4:3^2)^2

$$[ ( 3 ^ { 4 } \cdot 3 ^ { 7 } \cdot 3 ^ { 5 } ) ^ { 2 } : 3 ^ { 30 } ] ^ { 2 } : ( 3 ^ { 4 } : 3 ^ { 2 } ) ^ { 2 }$$

Evaluate

$$1$$

Solution Steps

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

$$\frac{\left(\frac{\left(3^{11}\times 3^{5}\right)^{2}}{3^{30}}\right)^{2}}{\left(\frac{3^{4}}{3^{2}}\right)^{2}}$$

To multiply powers of the same base, add their exponents. Add 11 and 5 to get 16.

$$\frac{\left(\frac{\left(3^{16}\right)^{2}}{3^{30}}\right)^{2}}{\left(\frac{3^{4}}{3^{2}}\right)^{2}}$$

To raise a power to another power, multiply the exponents. Multiply 16 and 2 to get 32.

$$\frac{\left(\frac{3^{32}}{3^{30}}\right)^{2}}{\left(\frac{3^{4}}{3^{2}}\right)^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 30 from 32 to get 2.

$$\frac{\left(3^{2}\right)^{2}}{\left(\frac{3^{4}}{3^{2}}\right)^{2}}$$

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

$$\frac{3^{4}}{\left(\frac{3^{4}}{3^{2}}\right)^{2}}$$

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

$$\frac{3^{4}}{\left(3^{2}\right)^{2}}$$

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

$$\frac{3^{4}}{3^{4}}$$

Divide 3^{4} by 3^{4} to get 1.

$$1$$

Factor

$$1$$