Solve {[16/9(3/4x^7y^4)^3]}^2

$$\{ [ \frac { 16 } { 9 } ( \frac { 3 } { 4 } x ^ { 7 } y ^ { 4 } ) ^ { 3 } ] \} ^ { 2 }$$

Evaluate

$$\frac{9y^{24}x^{42}}{16}$$

Solution Steps

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

$$\left(\frac{16}{9}\times \left(\frac{3}{4}\right)^{3}\left(x^{7}\right)^{3}\left(y^{4}\right)^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$\left(\frac{16}{9}\times \left(\frac{3}{4}\right)^{3}x^{21}\left(y^{4}\right)^{3}\right)^{2}$$

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

$$\left(\frac{16}{9}\times \left(\frac{3}{4}\right)^{3}x^{21}y^{12}\right)^{2}$$

Calculate \frac{3}{4} to the power of 3 and get \frac{27}{64}.

$$\left(\frac{16}{9}\times \frac{27}{64}x^{21}y^{12}\right)^{2}$$

Multiply \frac{16}{9} and \frac{27}{64} to get \frac{3}{4}.

$$\left(\frac{3}{4}x^{21}y^{12}\right)^{2}$$

Expand \left(\frac{3}{4}x^{21}y^{12}\right)^{2}.

$$\left(\frac{3}{4}\right)^{2}\left(x^{21}\right)^{2}\left(y^{12}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 21 and 2 to get 42.

$$\left(\frac{3}{4}\right)^{2}x^{42}\left(y^{12}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 12 and 2 to get 24.

$$\left(\frac{3}{4}\right)^{2}x^{42}y^{24}$$

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

$$\frac{9}{16}x^{42}y^{24}$$

Expand

$$\frac{9y^{24}x^{42}}{16}$$

Solution Steps

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

$$\left(\frac{16}{9}\times \left(\frac{3}{4}\right)^{3}\left(x^{7}\right)^{3}\left(y^{4}\right)^{3}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$\left(\frac{16}{9}\times \left(\frac{3}{4}\right)^{3}x^{21}\left(y^{4}\right)^{3}\right)^{2}$$

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

$$\left(\frac{16}{9}\times \left(\frac{3}{4}\right)^{3}x^{21}y^{12}\right)^{2}$$

Calculate \frac{3}{4} to the power of 3 and get \frac{27}{64}.

$$\left(\frac{16}{9}\times \frac{27}{64}x^{21}y^{12}\right)^{2}$$

Multiply \frac{16}{9} and \frac{27}{64} to get \frac{3}{4}.

$$\left(\frac{3}{4}x^{21}y^{12}\right)^{2}$$

Expand \left(\frac{3}{4}x^{21}y^{12}\right)^{2}.

$$\left(\frac{3}{4}\right)^{2}\left(x^{21}\right)^{2}\left(y^{12}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 21 and 2 to get 42.

$$\left(\frac{3}{4}\right)^{2}x^{42}\left(y^{12}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 12 and 2 to get 24.

$$\left(\frac{3}{4}\right)^{2}x^{42}y^{24}$$

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

$$\frac{9}{16}x^{42}y^{24}$$