Solve (4x^3y^3)^-2/2xy^-3

$$\frac { ( 4 x ^ { 3 } y ^ { 3 } ) ^ { - 2 } } { 2 x y ^ { - 3 } }$$

Evaluate

$$\frac{1}{32y^{3}x^{7}}$$

Solution Steps

Expand \left(4x^{3}y^{3}\right)^{-2}.

$$\frac{4^{-2}\left(x^{3}\right)^{-2}\left(y^{3}\right)^{-2}}{2xy^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -2 to get -6.

$$\frac{4^{-2}x^{-6}\left(y^{3}\right)^{-2}}{2xy^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -2 to get -6.

$$\frac{4^{-2}x^{-6}y^{-6}}{2xy^{-3}}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{\frac{1}{16}x^{-6}y^{-6}}{2xy^{-3}}$$

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

$$\frac{\frac{1}{16}}{2y^{3}x^{7}}$$

Express \frac{\frac{1}{16}}{2y^{3}x^{7}} as a single fraction.

$$\frac{1}{16\times 2y^{3}x^{7}}$$

Multiply 16 and 2 to get 32.

$$\frac{1}{32y^{3}x^{7}}$$

Expand

$$\frac{1}{32y^{3}x^{7}}$$

Solution Steps

Expand \left(4x^{3}y^{3}\right)^{-2}.

$$\frac{4^{-2}\left(x^{3}\right)^{-2}\left(y^{3}\right)^{-2}}{2xy^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -2 to get -6.

$$\frac{4^{-2}x^{-6}\left(y^{3}\right)^{-2}}{2xy^{-3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -2 to get -6.

$$\frac{4^{-2}x^{-6}y^{-6}}{2xy^{-3}}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{\frac{1}{16}x^{-6}y^{-6}}{2xy^{-3}}$$

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

$$\frac{\frac{1}{16}}{2y^{3}x^{7}}$$

Express \frac{\frac{1}{16}}{2y^{3}x^{7}} as a single fraction.

$$\frac{1}{16\times 2y^{3}x^{7}}$$

Multiply 16 and 2 to get 32.

$$\frac{1}{32y^{3}x^{7}}$$