Solve (xy^6/6)^-2

$$( \frac { x y ^ { 6 } } { 6 } ) ^ { - 2 }$$

Evaluate

$$\frac{36}{x^{2}y^{12}}$$

Solution Steps

To raise \frac{xy^{6}}{6} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(xy^{6}\right)^{-2}}{6^{-2}}$$

Expand \left(xy^{6}\right)^{-2}.

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

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

$$\frac{x^{-2}y^{-12}}{6^{-2}}$$

Calculate 6 to the power of -2 and get \frac{1}{36}.

$$\frac{x^{-2}y^{-12}}{\frac{1}{36}}$$

Divide x^{-2}y^{-12} by \frac{1}{36} by multiplying x^{-2}y^{-12} by the reciprocal of \frac{1}{36}.

$$x^{-2}y^{-12}\times 36$$

Expand

$$\frac{36}{x^{2}y^{12}}$$

Solution Steps

To raise \frac{xy^{6}}{6} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(xy^{6}\right)^{-2}}{6^{-2}}$$

Expand \left(xy^{6}\right)^{-2}.

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

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

$$\frac{x^{-2}y^{-12}}{6^{-2}}$$

Calculate 6 to the power of -2 and get \frac{1}{36}.

$$\frac{x^{-2}y^{-12}}{\frac{1}{36}}$$

Divide x^{-2}y^{-12} by \frac{1}{36} by multiplying x^{-2}y^{-12} by the reciprocal of \frac{1}{36}.

$$x^{-2}y^{-12}\times 36$$