Solve 9^-1(xy)^-4/8^-2(xy)^-2=

$$\frac { 9 ^ { - 1 } ( x y ) ^ { - 4 } } { 8 ^ { - 2 } ( x y ) ^ { - 2 } } =$$

Evaluate

$$\frac{64}{9\left(xy\right)^{2}}$$

Solution Steps

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

$$\frac{\frac{1}{9}}{8^{-2}\left(xy\right)^{2}}$$

Calculate 8 to the power of -2 and get \frac{1}{64}.

$$\frac{\frac{1}{9}}{\frac{1}{64}\left(xy\right)^{2}}$$

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

$$\frac{\frac{1}{9}}{\frac{1}{64}x^{2}y^{2}}$$

Express \frac{\frac{1}{9}}{\frac{1}{64}x^{2}y^{2}} as a single fraction.

$$\frac{1}{9\times \frac{1}{64}x^{2}y^{2}}$$

Multiply 9 and \frac{1}{64} to get \frac{9}{64}.

$$\frac{1}{\frac{9}{64}x^{2}y^{2}}$$

Expand

$$\frac{64}{9\left(xy\right)^{2}}$$

Solution Steps

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

$$\frac{\frac{1}{9}}{8^{-2}\left(xy\right)^{2}}$$

Calculate 8 to the power of -2 and get \frac{1}{64}.

$$\frac{\frac{1}{9}}{\frac{1}{64}\left(xy\right)^{2}}$$

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

$$\frac{\frac{1}{9}}{\frac{1}{64}x^{2}y^{2}}$$

Express \frac{\frac{1}{9}}{\frac{1}{64}x^{2}y^{2}} as a single fraction.

$$\frac{1}{9\times \frac{1}{64}x^{2}y^{2}}$$

Multiply 9 and \frac{1}{64} to get \frac{9}{64}.

$$\frac{1}{\frac{9}{64}x^{2}y^{2}}$$