Solve (frac{45x^{3}y^{-2}z^{4}}{9x^-3y^8z^6})^6

$$( \frac { 45 x ^ { 3 } y ^ { - 2 } z ^ { 4 } } { 9 x ^ { - 3 } y ^ { 8 } z ^ { 6 } } ) ^ { 6 }$$

Evaluate

$$\frac{15625x^{36}}{z^{12}y^{60}}$$

Solution Steps

Cancel out 9z^{4} in both numerator and denominator.

$$\left(\frac{5y^{-2}x^{3}}{x^{-3}z^{2}y^{8}}\right)^{6}$$

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

$$\left(\frac{5y^{-2}x^{6}}{z^{2}y^{8}}\right)^{6}$$

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

$$\left(\frac{5x^{6}}{z^{2}y^{10}}\right)^{6}$$

To raise \frac{5x^{6}}{z^{2}y^{10}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5x^{6}\right)^{6}}{\left(z^{2}y^{10}\right)^{6}}$$

Expand \left(5x^{6}\right)^{6}.

$$\frac{5^{6}\left(x^{6}\right)^{6}}{\left(z^{2}y^{10}\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 6 to get 36.

$$\frac{5^{6}x^{36}}{\left(z^{2}y^{10}\right)^{6}}$$

Calculate 5 to the power of 6 and get 15625.

$$\frac{15625x^{36}}{\left(z^{2}y^{10}\right)^{6}}$$

Expand \left(z^{2}y^{10}\right)^{6}.

$$\frac{15625x^{36}}{\left(z^{2}\right)^{6}\left(y^{10}\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$\frac{15625x^{36}}{z^{12}\left(y^{10}\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 10 and 6 to get 60.

$$\frac{15625x^{36}}{z^{12}y^{60}}$$

Expand

$$\frac{15625x^{36}}{z^{12}y^{60}}$$

Solution Steps

Cancel out 9z^{4} in both numerator and denominator.

$$\left(\frac{5y^{-2}x^{3}}{x^{-3}z^{2}y^{8}}\right)^{6}$$

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

$$\left(\frac{5y^{-2}x^{6}}{z^{2}y^{8}}\right)^{6}$$

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

$$\left(\frac{5x^{6}}{z^{2}y^{10}}\right)^{6}$$

To raise \frac{5x^{6}}{z^{2}y^{10}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(5x^{6}\right)^{6}}{\left(z^{2}y^{10}\right)^{6}}$$

Expand \left(5x^{6}\right)^{6}.

$$\frac{5^{6}\left(x^{6}\right)^{6}}{\left(z^{2}y^{10}\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 6 to get 36.

$$\frac{5^{6}x^{36}}{\left(z^{2}y^{10}\right)^{6}}$$

Calculate 5 to the power of 6 and get 15625.

$$\frac{15625x^{36}}{\left(z^{2}y^{10}\right)^{6}}$$

Expand \left(z^{2}y^{10}\right)^{6}.

$$\frac{15625x^{36}}{\left(z^{2}\right)^{6}\left(y^{10}\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$\frac{15625x^{36}}{z^{12}\left(y^{10}\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 10 and 6 to get 60.

$$\frac{15625x^{36}}{z^{12}y^{60}}$$