Solve [(3x^2*3x^5)^2]^2

$$[ ( 3 x ^ { 2 } \times 3 x ^ { 5 } ) ^ { 2 } ] ^ { 2 }$$

Evaluate

$$6561x^{28}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

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

Multiply 3 and 3 to get 9.

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

Expand \left(9x^{7}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\left(9^{2}x^{14}\right)^{2}$$

Calculate 9 to the power of 2 and get 81.

$$\left(81x^{14}\right)^{2}$$

Expand \left(81x^{14}\right)^{2}.

$$81^{2}\left(x^{14}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 14 and 2 to get 28.

$$81^{2}x^{28}$$

Calculate 81 to the power of 2 and get 6561.

$$6561x^{28}$$

Expand

$$6561x^{28}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

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

Multiply 3 and 3 to get 9.

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

Expand \left(9x^{7}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 7 and 2 to get 14.

$$\left(9^{2}x^{14}\right)^{2}$$

Calculate 9 to the power of 2 and get 81.

$$\left(81x^{14}\right)^{2}$$

Expand \left(81x^{14}\right)^{2}.

$$81^{2}\left(x^{14}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 14 and 2 to get 28.

$$81^{2}x^{28}$$

Calculate 81 to the power of 2 and get 6561.

$$6561x^{28}$$