Solve (-3x^{3}y^{4})^2*(-1/3ax^2y^3)^3

$$( - 3 x ^ { 3 } y ^ { 4 } ) ^ { 2 } \cdot ( - \frac { 1 } { 3 } a x ^ { 2 } y ^ { 3 } ) ^ { 3 }$$

Evaluate

$$-\frac{a^{3}x^{12}y^{17}}{3}$$

Solution Steps

Expand \left(-3x^{3}y^{4}\right)^{2}.

$$\left(-3\right)^{2}\left(x^{3}\right)^{2}\left(y^{4}\right)^{2}\left(-\frac{1}{3}ax^{2}y^{3}\right)^{3}$$

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

$$\left(-3\right)^{2}x^{6}\left(y^{4}\right)^{2}\left(-\frac{1}{3}ax^{2}y^{3}\right)^{3}$$

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

$$\left(-3\right)^{2}x^{6}y^{8}\left(-\frac{1}{3}ax^{2}y^{3}\right)^{3}$$

Calculate -3 to the power of 2 and get 9.

$$9x^{6}y^{8}\left(-\frac{1}{3}ax^{2}y^{3}\right)^{3}$$

Expand \left(-\frac{1}{3}ax^{2}y^{3}\right)^{3}.

$$9x^{6}y^{8}\left(-\frac{1}{3}\right)^{3}a^{3}\left(x^{2}\right)^{3}\left(y^{3}\right)^{3}$$

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

$$9x^{6}y^{8}\left(-\frac{1}{3}\right)^{3}a^{3}x^{6}\left(y^{3}\right)^{3}$$

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

$$9x^{6}y^{8}\left(-\frac{1}{3}\right)^{3}a^{3}x^{6}y^{9}$$

Calculate -\frac{1}{3} to the power of 3 and get -\frac{1}{27}.

$$9x^{6}y^{8}\left(-\frac{1}{27}\right)a^{3}x^{6}y^{9}$$

Multiply 9 and -\frac{1}{27} to get -\frac{1}{3}.

$$-\frac{1}{3}x^{6}y^{8}a^{3}x^{6}y^{9}$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$-\frac{1}{3}x^{12}y^{8}a^{3}y^{9}$$

To multiply powers of the same base, add their exponents. Add 8 and 9 to get 17.

$$-\frac{1}{3}x^{12}y^{17}a^{3}$$

Expand

$$-\frac{a^{3}x^{12}y^{17}}{3}$$

Solution Steps

Expand \left(-3x^{3}y^{4}\right)^{2}.

$$\left(-3\right)^{2}\left(x^{3}\right)^{2}\left(y^{4}\right)^{2}\left(-\frac{1}{3}ax^{2}y^{3}\right)^{3}$$

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

$$\left(-3\right)^{2}x^{6}\left(y^{4}\right)^{2}\left(-\frac{1}{3}ax^{2}y^{3}\right)^{3}$$

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

$$\left(-3\right)^{2}x^{6}y^{8}\left(-\frac{1}{3}ax^{2}y^{3}\right)^{3}$$

Calculate -3 to the power of 2 and get 9.

$$9x^{6}y^{8}\left(-\frac{1}{3}ax^{2}y^{3}\right)^{3}$$

Expand \left(-\frac{1}{3}ax^{2}y^{3}\right)^{3}.

$$9x^{6}y^{8}\left(-\frac{1}{3}\right)^{3}a^{3}\left(x^{2}\right)^{3}\left(y^{3}\right)^{3}$$

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

$$9x^{6}y^{8}\left(-\frac{1}{3}\right)^{3}a^{3}x^{6}\left(y^{3}\right)^{3}$$

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

$$9x^{6}y^{8}\left(-\frac{1}{3}\right)^{3}a^{3}x^{6}y^{9}$$

Calculate -\frac{1}{3} to the power of 3 and get -\frac{1}{27}.

$$9x^{6}y^{8}\left(-\frac{1}{27}\right)a^{3}x^{6}y^{9}$$

Multiply 9 and -\frac{1}{27} to get -\frac{1}{3}.

$$-\frac{1}{3}x^{6}y^{8}a^{3}x^{6}y^{9}$$

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$-\frac{1}{3}x^{12}y^{8}a^{3}y^{9}$$

To multiply powers of the same base, add their exponents. Add 8 and 9 to get 17.

$$-\frac{1}{3}x^{12}y^{17}a^{3}$$