Solve [(3^{2}x^2)*(5^2x^6)]^-3

$$[ ( 3 ^ { 2 } x ^ { 2 } ) \cdot ( 5 ^ { 2 } x ^ { 6 } ) ] ^ { - 3 }$$

Evaluate

$$\frac{1}{11390625x^{24}}$$

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 \frac{1}{11390625}.

$$\frac{1}{11390625}x^{-24}$$

Expand

$$\frac{1}{11390625x^{24}}$$

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 \frac{1}{11390625}.

$$\frac{1}{11390625}x^{-24}$$