Solve (6/9x^2y^7)^4xy

$$( \frac { 6 } { 9 } x ^ { 2 } y ^ { 7 } ) ^ { 4 } x y$$

Evaluate

$$\frac{16x^{9}y^{29}}{81}$$

Solution Steps

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

$$\left(\frac{2}{3}x^{2}y^{7}\right)^{4}xy$$

Expand \left(\frac{2}{3}x^{2}y^{7}\right)^{4}.

$$\left(\frac{2}{3}\right)^{4}\left(x^{2}\right)^{4}\left(y^{7}\right)^{4}xy$$

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

$$\left(\frac{2}{3}\right)^{4}x^{8}\left(y^{7}\right)^{4}xy$$

To raise a power to another power, multiply the exponents. Multiply 7 and 4 to get 28.

$$\left(\frac{2}{3}\right)^{4}x^{8}y^{28}xy$$

Calculate \frac{2}{3} to the power of 4 and get \frac{16}{81}.

$$\frac{16}{81}x^{8}y^{28}xy$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$\frac{16}{81}x^{9}y^{28}y$$

To multiply powers of the same base, add their exponents. Add 28 and 1 to get 29.

$$\frac{16}{81}x^{9}y^{29}$$

Expand

$$\frac{16x^{9}y^{29}}{81}$$

Solution Steps

Reduce the fraction \frac{6}{9} to lowest terms by extracting and canceling out 3.

$$\left(\frac{2}{3}x^{2}y^{7}\right)^{4}xy$$

Expand \left(\frac{2}{3}x^{2}y^{7}\right)^{4}.

$$\left(\frac{2}{3}\right)^{4}\left(x^{2}\right)^{4}\left(y^{7}\right)^{4}xy$$

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

$$\left(\frac{2}{3}\right)^{4}x^{8}\left(y^{7}\right)^{4}xy$$

To raise a power to another power, multiply the exponents. Multiply 7 and 4 to get 28.

$$\left(\frac{2}{3}\right)^{4}x^{8}y^{28}xy$$

Calculate \frac{2}{3} to the power of 4 and get \frac{16}{81}.

$$\frac{16}{81}x^{8}y^{28}xy$$

To multiply powers of the same base, add their exponents. Add 8 and 1 to get 9.

$$\frac{16}{81}x^{9}y^{28}y$$

To multiply powers of the same base, add their exponents. Add 28 and 1 to get 29.

$$\frac{16}{81}x^{9}y^{29}$$