Solve (4/3xy^2)^2*(-9xz^3)

$$( \frac { 4 } { 3 } x y ^ { 2 } ) ^ { 2 } \cdot ( - 9 x z ^ { 3 } )$$

Evaluate

$$-16y^{4}\left(xz\right)^{3}$$

Solution Steps

Expand \left(\frac{4}{3}xy^{2}\right)^{2}.

$$\left(\frac{4}{3}\right)^{2}x^{2}\left(y^{2}\right)^{2}\left(-9\right)xz^{3}$$

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

$$\left(\frac{4}{3}\right)^{2}x^{2}y^{4}\left(-9\right)xz^{3}$$

Calculate \frac{4}{3} to the power of 2 and get \frac{16}{9}.

$$\frac{16}{9}x^{2}y^{4}\left(-9\right)xz^{3}$$

Multiply \frac{16}{9} and -9 to get -16.

$$-16x^{2}y^{4}xz^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$-16x^{3}y^{4}z^{3}$$

Expand

$$-16y^{4}\left(xz\right)^{3}$$

Solution Steps

Expand \left(\frac{4}{3}xy^{2}\right)^{2}.

$$\left(\frac{4}{3}\right)^{2}x^{2}\left(y^{2}\right)^{2}\left(-9\right)xz^{3}$$

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

$$\left(\frac{4}{3}\right)^{2}x^{2}y^{4}\left(-9\right)xz^{3}$$

Calculate \frac{4}{3} to the power of 2 and get \frac{16}{9}.

$$\frac{16}{9}x^{2}y^{4}\left(-9\right)xz^{3}$$

Multiply \frac{16}{9} and -9 to get -16.

$$-16x^{2}y^{4}xz^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$-16x^{3}y^{4}z^{3}$$