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

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

Evaluate

$$81$$

Solution Steps

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

$$\left(\frac{3\times 3^{8}}{3^{7}}\right)^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 8 to get 9.

$$\left(\frac{3^{9}}{3^{7}}\right)^{2}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 7 from 9 to get 2.

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

Calculate 3 to the power of 2 and get 9.

$$9^{2}$$

Calculate 9 to the power of 2 and get 81.

$$81$$

Factor

$$3^{4}$$