Solve {left(-1/3x^2yright)}^3*left(-3xy^3right)^4

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

Evaluate

$$-3x^{10}y^{15}$$

Solution Steps

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

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

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

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

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

$$-\frac{1}{27}x^{6}y^{3}\left(-3xy^{3}\right)^{4}$$

Expand \left(-3xy^{3}\right)^{4}.

$$-\frac{1}{27}x^{6}y^{3}\left(-3\right)^{4}x^{4}\left(y^{3}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$-\frac{1}{27}x^{6}y^{3}\left(-3\right)^{4}x^{4}y^{12}$$

Calculate -3 to the power of 4 and get 81.

$$-\frac{1}{27}x^{6}y^{3}\times 81x^{4}y^{12}$$

Multiply -\frac{1}{27} and 81 to get -3.

$$-3x^{6}y^{3}x^{4}y^{12}$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$-3x^{10}y^{3}y^{12}$$

To multiply powers of the same base, add their exponents. Add 3 and 12 to get 15.

$$-3x^{10}y^{15}$$

Expand

$$-3x^{10}y^{15}$$

Solution Steps

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

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

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

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

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

$$-\frac{1}{27}x^{6}y^{3}\left(-3xy^{3}\right)^{4}$$

Expand \left(-3xy^{3}\right)^{4}.

$$-\frac{1}{27}x^{6}y^{3}\left(-3\right)^{4}x^{4}\left(y^{3}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 4 to get 12.

$$-\frac{1}{27}x^{6}y^{3}\left(-3\right)^{4}x^{4}y^{12}$$

Calculate -3 to the power of 4 and get 81.

$$-\frac{1}{27}x^{6}y^{3}\times 81x^{4}y^{12}$$

Multiply -\frac{1}{27} and 81 to get -3.

$$-3x^{6}y^{3}x^{4}y^{12}$$

To multiply powers of the same base, add their exponents. Add 6 and 4 to get 10.

$$-3x^{10}y^{3}y^{12}$$

To multiply powers of the same base, add their exponents. Add 3 and 12 to get 15.

$$-3x^{10}y^{15}$$