Solve {left(3^2x^25^2x^6right)}^3

$${ \left( { 3 }^{ 2 } { x }^{ 2 } { 5 }^{ 2 } { x }^{ 6 } \right) }^{ 3 }$$

Evaluate

$$11390625x^{24}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$\left(3^{2}x^{8}\times 5^{2}\right)^{3}$$

Calculate 3 to the power of 2 and get 9.

$$\left(9x^{8}\times 5^{2}\right)^{3}$$

Calculate 5 to the power of 2 and get 25.

$$\left(9x^{8}\times 25\right)^{3}$$

Multiply 9 and 25 to get 225.

$$\left(225x^{8}\right)^{3}$$

Expand \left(225x^{8}\right)^{3}.

$$225^{3}\left(x^{8}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 3 to get 24.

$$225^{3}x^{24}$$

Calculate 225 to the power of 3 and get 11390625.

$$11390625x^{24}$$

Expand

$$11390625x^{24}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$\left(3^{2}x^{8}\times 5^{2}\right)^{3}$$

Calculate 3 to the power of 2 and get 9.

$$\left(9x^{8}\times 5^{2}\right)^{3}$$

Calculate 5 to the power of 2 and get 25.

$$\left(9x^{8}\times 25\right)^{3}$$

Multiply 9 and 25 to get 225.

$$\left(225x^{8}\right)^{3}$$

Expand \left(225x^{8}\right)^{3}.

$$225^{3}\left(x^{8}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 3 to get 24.

$$225^{3}x^{24}$$

Calculate 225 to the power of 3 and get 11390625.

$$11390625x^{24}$$