Solve frac{(2x^{3}*2x^{3}y^4)^-2}{2x^2y^4}

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

Evaluate

$$\frac{1}{32y^{12}x^{14}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

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

Multiply 2 and 2 to get 4.

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

Expand \left(4x^{6}y^{4}\right)^{-2}.

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

To raise a power to another power, multiply the exponents. Multiply 6 and -2 to get -12.

$$\frac{4^{-2}x^{-12}\left(y^{4}\right)^{-2}}{2x^{2}y^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$\frac{4^{-2}x^{-12}y^{-8}}{2x^{2}y^{4}}$$

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

$$\frac{\frac{1}{16}x^{-12}y^{-8}}{2x^{2}y^{4}}$$

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

$$\frac{\frac{1}{16}}{2y^{12}x^{14}}$$

Express \frac{\frac{1}{16}}{2y^{12}x^{14}} as a single fraction.

$$\frac{1}{16\times 2y^{12}x^{14}}$$

Multiply 16 and 2 to get 32.

$$\frac{1}{32y^{12}x^{14}}$$

Expand

$$\frac{1}{32y^{12}x^{14}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

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

Multiply 2 and 2 to get 4.

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

Expand \left(4x^{6}y^{4}\right)^{-2}.

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

To raise a power to another power, multiply the exponents. Multiply 6 and -2 to get -12.

$$\frac{4^{-2}x^{-12}\left(y^{4}\right)^{-2}}{2x^{2}y^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and -2 to get -8.

$$\frac{4^{-2}x^{-12}y^{-8}}{2x^{2}y^{4}}$$

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

$$\frac{\frac{1}{16}x^{-12}y^{-8}}{2x^{2}y^{4}}$$

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

$$\frac{\frac{1}{16}}{2y^{12}x^{14}}$$

Express \frac{\frac{1}{16}}{2y^{12}x^{14}} as a single fraction.

$$\frac{1}{16\times 2y^{12}x^{14}}$$

Multiply 16 and 2 to get 32.

$$\frac{1}{32y^{12}x^{14}}$$