Solve (2x^2/3x^-3)^-2=

$$( \frac { 2 x ^ { 2 } } { 3 x ^ { - 3 } } ) ^ { - 2 } =$$

Evaluate

$$\frac{9}{4x^{10}}$$

Solution Steps

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

$$\left(\frac{2x^{5}}{3}\right)^{-2}$$

To raise \frac{2x^{5}}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2x^{5}\right)^{-2}}{3^{-2}}$$

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

$$\frac{2^{-2}\left(x^{5}\right)^{-2}}{3^{-2}}$$

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

$$\frac{2^{-2}x^{-10}}{3^{-2}}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{\frac{1}{4}x^{-10}}{3^{-2}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{4}x^{-10}}{\frac{1}{9}}$$

Divide \frac{1}{4}x^{-10} by \frac{1}{9} by multiplying \frac{1}{4}x^{-10} by the reciprocal of \frac{1}{9}.

$$\frac{1}{4}x^{-10}\times 9$$

Multiply \frac{1}{4} and 9 to get \frac{9}{4}.

$$\frac{9}{4}x^{-10}$$

Expand

$$\frac{9}{4x^{10}}$$

Solution Steps

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

$$\left(\frac{2x^{5}}{3}\right)^{-2}$$

To raise \frac{2x^{5}}{3} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2x^{5}\right)^{-2}}{3^{-2}}$$

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

$$\frac{2^{-2}\left(x^{5}\right)^{-2}}{3^{-2}}$$

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

$$\frac{2^{-2}x^{-10}}{3^{-2}}$$

Calculate 2 to the power of -2 and get \frac{1}{4}.

$$\frac{\frac{1}{4}x^{-10}}{3^{-2}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{\frac{1}{4}x^{-10}}{\frac{1}{9}}$$

Divide \frac{1}{4}x^{-10} by \frac{1}{9} by multiplying \frac{1}{4}x^{-10} by the reciprocal of \frac{1}{9}.

$$\frac{1}{4}x^{-10}\times 9$$

Multiply \frac{1}{4} and 9 to get \frac{9}{4}.

$$\frac{9}{4}x^{-10}$$