Solve [(-ax^2y^3)^3]^2

$$[ ( - a x ^ { 2 } y ^ { 3 } ) ^ { 3 } ] ^ { 2 }$$

Evaluate

$$a^{6}x^{12}y^{18}$$

Solution Steps

Expand \left(\left(-a\right)x^{2}y^{3}\right)^{3}.

$$\left(\left(-a\right)^{3}\left(x^{2}\right)^{3}\left(y^{3}\right)^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\left(\left(-a\right)^{3}x^{6}\left(y^{3}\right)^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\left(\left(-a\right)^{3}x^{6}y^{9}\right)^{2}$$

Expand \left(\left(-a\right)^{3}x^{6}y^{9}\right)^{2}.

$$\left(\left(-a\right)^{3}\right)^{2}\left(x^{6}\right)^{2}\left(y^{9}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\left(-a\right)^{6}\left(x^{6}\right)^{2}\left(y^{9}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\left(-a\right)^{6}x^{12}\left(y^{9}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 2 to get 18.

$$\left(-a\right)^{6}x^{12}y^{18}$$

Expand \left(-a\right)^{6}.

$$\left(-1\right)^{6}a^{6}x^{12}y^{18}$$

Calculate -1 to the power of 6 and get 1.

$$1a^{6}x^{12}y^{18}$$

For any term t, t\times 1=t and 1t=t.

$$a^{6}x^{12}y^{18}$$

Expand

$$a^{6}x^{12}y^{18}$$

Solution Steps

Expand \left(\left(-a\right)x^{2}y^{3}\right)^{3}.

$$\left(\left(-a\right)^{3}\left(x^{2}\right)^{3}\left(y^{3}\right)^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\left(\left(-a\right)^{3}x^{6}\left(y^{3}\right)^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\left(\left(-a\right)^{3}x^{6}y^{9}\right)^{2}$$

Expand \left(\left(-a\right)^{3}x^{6}y^{9}\right)^{2}.

$$\left(\left(-a\right)^{3}\right)^{2}\left(x^{6}\right)^{2}\left(y^{9}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\left(-a\right)^{6}\left(x^{6}\right)^{2}\left(y^{9}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\left(-a\right)^{6}x^{12}\left(y^{9}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 2 to get 18.

$$\left(-a\right)^{6}x^{12}y^{18}$$

Expand \left(-a\right)^{6}.

$$\left(-1\right)^{6}a^{6}x^{12}y^{18}$$

Calculate -1 to the power of 6 and get 1.

$$1a^{6}x^{12}y^{18}$$

For any term t, t\times 1=t and 1t=t.

$$a^{6}x^{12}y^{18}$$