Solve left(3x^-1right)^-2/left(3x^2right)^-2

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

Evaluate

$$x^{6}$$

Solution Steps

Expand \left(3x^{-1}\right)^{-2}.

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

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

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

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

$$\frac{\frac{1}{9}x^{2}}{\left(3x^{2}\right)^{-2}}$$

Expand \left(3x^{2}\right)^{-2}.

$$\frac{\frac{1}{9}x^{2}}{3^{-2}\left(x^{2}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -2 to get -4.

$$\frac{\frac{1}{9}x^{2}}{3^{-2}x^{-4}}$$

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

$$\frac{\frac{1}{9}x^{2}}{\frac{1}{9}x^{-4}}$$

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

$$\frac{\frac{1}{9}x^{6}}{\frac{1}{9}}$$

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

$$\frac{x^{6}}{\left(\frac{1}{9}\right)^{0}}$$

Calculate \frac{1}{9} to the power of 0 and get 1.

$$\frac{x^{6}}{1}$$

Anything divided by one gives itself.

$$x^{6}$$

Expand

$$x^{6}$$

Solution Steps

Expand \left(3x^{-1}\right)^{-2}.

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

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

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

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

$$\frac{\frac{1}{9}x^{2}}{\left(3x^{2}\right)^{-2}}$$

Expand \left(3x^{2}\right)^{-2}.

$$\frac{\frac{1}{9}x^{2}}{3^{-2}\left(x^{2}\right)^{-2}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and -2 to get -4.

$$\frac{\frac{1}{9}x^{2}}{3^{-2}x^{-4}}$$

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

$$\frac{\frac{1}{9}x^{2}}{\frac{1}{9}x^{-4}}$$

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

$$\frac{\frac{1}{9}x^{6}}{\frac{1}{9}}$$

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

$$\frac{x^{6}}{\left(\frac{1}{9}\right)^{0}}$$

Calculate \frac{1}{9} to the power of 0 and get 1.

$$\frac{x^{6}}{1}$$

Anything divided by one gives itself.

$$x^{6}$$