Solve (2x^{-1}y^{-6})^4*(2x^3y^3)^-4

$$( 2 x ^ { - 1 } y ^ { - 6 } ) ^ { 4 } \cdot ( 2 x ^ { 3 } y ^ { 3 } ) ^ { - 4 }$$

Evaluate

$$\frac{1}{x^{16}y^{36}}$$

Solution Steps

Expand \left(2x^{-1}y^{-6}\right)^{4}.

$$2^{4}\left(x^{-1}\right)^{4}\left(y^{-6}\right)^{4}\times \left(2x^{3}y^{3}\right)^{-4}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 4 to get -4.

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

To raise a power to another power, multiply the exponents. Multiply -6 and 4 to get -24.

$$2^{4}x^{-4}y^{-24}\times \left(2x^{3}y^{3}\right)^{-4}$$

Calculate 2 to the power of 4 and get 16.

$$16x^{-4}y^{-24}\times \left(2x^{3}y^{3}\right)^{-4}$$

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

$$16x^{-4}y^{-24}\times 2^{-4}\left(x^{3}\right)^{-4}\left(y^{3}\right)^{-4}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -4 to get -12.

$$16x^{-4}y^{-24}\times 2^{-4}x^{-12}\left(y^{3}\right)^{-4}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -4 to get -12.

$$16x^{-4}y^{-24}\times 2^{-4}x^{-12}y^{-12}$$

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

$$16x^{-4}y^{-24}\times \frac{1}{16}x^{-12}y^{-12}$$

Multiply 16 and \frac{1}{16} to get 1.

$$x^{-4}y^{-24}x^{-12}y^{-12}$$

To multiply powers of the same base, add their exponents. Add -4 and -12 to get -16.

$$x^{-16}y^{-24}y^{-12}$$

To multiply powers of the same base, add their exponents. Add -24 and -12 to get -36.

$$x^{-16}y^{-36}$$

Expand

$$\frac{1}{x^{16}y^{36}}$$

Solution Steps

Expand \left(2x^{-1}y^{-6}\right)^{4}.

$$2^{4}\left(x^{-1}\right)^{4}\left(y^{-6}\right)^{4}\times \left(2x^{3}y^{3}\right)^{-4}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 4 to get -4.

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

To raise a power to another power, multiply the exponents. Multiply -6 and 4 to get -24.

$$2^{4}x^{-4}y^{-24}\times \left(2x^{3}y^{3}\right)^{-4}$$

Calculate 2 to the power of 4 and get 16.

$$16x^{-4}y^{-24}\times \left(2x^{3}y^{3}\right)^{-4}$$

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

$$16x^{-4}y^{-24}\times 2^{-4}\left(x^{3}\right)^{-4}\left(y^{3}\right)^{-4}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -4 to get -12.

$$16x^{-4}y^{-24}\times 2^{-4}x^{-12}\left(y^{3}\right)^{-4}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -4 to get -12.

$$16x^{-4}y^{-24}\times 2^{-4}x^{-12}y^{-12}$$

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

$$16x^{-4}y^{-24}\times \frac{1}{16}x^{-12}y^{-12}$$

Multiply 16 and \frac{1}{16} to get 1.

$$x^{-4}y^{-24}x^{-12}y^{-12}$$

To multiply powers of the same base, add their exponents. Add -4 and -12 to get -16.

$$x^{-16}y^{-24}y^{-12}$$

To multiply powers of the same base, add their exponents. Add -24 and -12 to get -36.

$$x^{-16}y^{-36}$$