Solve [(frac{x^{-2}y^{3}t}{x^{-3}y^-2t^2})^2]^-1

$$[ ( \frac { x ^ { - 2 } y ^ { 3 } t } { x ^ { - 3 } y ^ { - 2 } t ^ { 2 } } ) ^ { 2 } ] ^ { - 1 }$$

Evaluate

$$\frac{\left(\frac{t}{x}\right)^{2}}{y^{10}}$$

Solution Steps

Cancel out t in both numerator and denominator.

$$\left(\left(\frac{x^{-2}y^{3}}{x^{-3}y^{-2}t}\right)^{2}\right)^{-1}$$

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

$$\left(\left(\frac{x^{1}y^{5}}{t}\right)^{2}\right)^{-1}$$

Calculate x to the power of 1 and get x.

$$\left(\left(\frac{xy^{5}}{t}\right)^{2}\right)^{-1}$$

To raise \frac{xy^{5}}{t} to a power, raise both numerator and denominator to the power and then divide.

$$\left(\frac{\left(xy^{5}\right)^{2}}{t^{2}}\right)^{-1}$$

To raise \frac{\left(xy^{5}\right)^{2}}{t^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(\left(xy^{5}\right)^{2}\right)^{-1}}{\left(t^{2}\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$\frac{\left(xy^{5}\right)^{-2}}{\left(t^{2}\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$\frac{\left(xy^{5}\right)^{-2}}{t^{-2}}$$

Expand \left(xy^{5}\right)^{-2}.

$$\frac{x^{-2}\left(y^{5}\right)^{-2}}{t^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -2 to get -10.

$$\frac{x^{-2}y^{-10}}{t^{-2}}$$

Expand

$$\frac{\left(\frac{t}{x}\right)^{2}}{y^{10}}$$

Solution Steps

Cancel out t in both numerator and denominator.

$$\left(\left(\frac{x^{-2}y^{3}}{x^{-3}y^{-2}t}\right)^{2}\right)^{-1}$$

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

$$\left(\left(\frac{x^{1}y^{5}}{t}\right)^{2}\right)^{-1}$$

Calculate x to the power of 1 and get x.

$$\left(\left(\frac{xy^{5}}{t}\right)^{2}\right)^{-1}$$

To raise \frac{xy^{5}}{t} to a power, raise both numerator and denominator to the power and then divide.

$$\left(\frac{\left(xy^{5}\right)^{2}}{t^{2}}\right)^{-1}$$

To raise \frac{\left(xy^{5}\right)^{2}}{t^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(\left(xy^{5}\right)^{2}\right)^{-1}}{\left(t^{2}\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$\frac{\left(xy^{5}\right)^{-2}}{\left(t^{2}\right)^{-1}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -1 to get -2.

$$\frac{\left(xy^{5}\right)^{-2}}{t^{-2}}$$

Expand \left(xy^{5}\right)^{-2}.

$$\frac{x^{-2}\left(y^{5}\right)^{-2}}{t^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and -2 to get -10.

$$\frac{x^{-2}y^{-10}}{t^{-2}}$$