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

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

Evaluate

$$-\frac{8}{27}\approx -0.296296296$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

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

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

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

Use the Commutative Property of Multiplication.

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

To raise a power to another power, multiply the exponents.

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

Multiply -2 times 3.

$$\left(-2\right)^{3}\times 3^{-3}x^{-6}x^{-2\left(-3\right)}$$

Multiply -2 times -3.

$$\left(-2\right)^{3}\times 3^{-3}x^{-6}x^{6}$$

To multiply powers of the same base, add their exponents.

$$\left(-2\right)^{3}\times 3^{-3}x^{-6+6}$$

Add the exponents -6 and 6.

$$\left(-2\right)^{3}\times 3^{-3}x^{0}$$

Raise -2 to the power 3.

$$-8\times 3^{-3}x^{0}$$

Raise 3 to the power -3.

$$-8\times \frac{1}{27}x^{0}$$

Multiply -8 times \frac{1}{27}.

$$-\frac{8}{27}x^{0}$$

For any term t except 0, t^{0}=1.

$$-\frac{8}{27}$$

Factor

$$-\frac{8}{27} = -0.2962962962962963$$