Solve [frac{6x^{3}y^{5}x^{4}}{3^3x^2yx^-3}]^3

$$[ \frac { 6 x ^ { 3 } y ^ { 5 } x ^ { 4 } } { 3 ^ { 3 } x ^ { 2 } y x ^ { - 3 } } ] ^ { 3 }$$

Evaluate

$$\frac{8y^{12}x^{24}}{729}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\left(\frac{6x^{7}y^{5}}{3^{3}x^{2}yx^{-3}}\right)^{3}$$

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

$$\left(\frac{6x^{7}y^{5}}{3^{3}x^{-1}y}\right)^{3}$$

Cancel out y in both numerator and denominator.

$$\left(\frac{6y^{4}x^{7}}{3^{3}\times \frac{1}{x}}\right)^{3}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\left(\frac{6y^{4}x^{8}}{3^{3}}\right)^{3}$$

Calculate 3 to the power of 3 and get 27.

$$\left(\frac{6y^{4}x^{8}}{27}\right)^{3}$$

Divide 6y^{4}x^{8} by 27 to get \frac{2}{9}y^{4}x^{8}.

$$\left(\frac{2}{9}y^{4}x^{8}\right)^{3}$$

Expand \left(\frac{2}{9}y^{4}x^{8}\right)^{3}.

$$\left(\frac{2}{9}\right)^{3}\left(y^{4}\right)^{3}\left(x^{8}\right)^{3}$$

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

$$\left(\frac{2}{9}\right)^{3}y^{12}\left(x^{8}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 3 to get 24.

$$\left(\frac{2}{9}\right)^{3}y^{12}x^{24}$$

Calculate \frac{2}{9} to the power of 3 and get \frac{8}{729}.

$$\frac{8}{729}y^{12}x^{24}$$

Expand

$$\frac{8y^{12}x^{24}}{729}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\left(\frac{6x^{7}y^{5}}{3^{3}x^{2}yx^{-3}}\right)^{3}$$

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

$$\left(\frac{6x^{7}y^{5}}{3^{3}x^{-1}y}\right)^{3}$$

Cancel out y in both numerator and denominator.

$$\left(\frac{6y^{4}x^{7}}{3^{3}\times \frac{1}{x}}\right)^{3}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\left(\frac{6y^{4}x^{8}}{3^{3}}\right)^{3}$$

Calculate 3 to the power of 3 and get 27.

$$\left(\frac{6y^{4}x^{8}}{27}\right)^{3}$$

Divide 6y^{4}x^{8} by 27 to get \frac{2}{9}y^{4}x^{8}.

$$\left(\frac{2}{9}y^{4}x^{8}\right)^{3}$$

Expand \left(\frac{2}{9}y^{4}x^{8}\right)^{3}.

$$\left(\frac{2}{9}\right)^{3}\left(y^{4}\right)^{3}\left(x^{8}\right)^{3}$$

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

$$\left(\frac{2}{9}\right)^{3}y^{12}\left(x^{8}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 3 to get 24.

$$\left(\frac{2}{9}\right)^{3}y^{12}x^{24}$$

Calculate \frac{2}{9} to the power of 3 and get \frac{8}{729}.

$$\frac{8}{729}y^{12}x^{24}$$