Solve (2x^{-2}y^3)^42x^19y^-6

$$( 2 x ^ { - 2 } y ^ { 3 } ) ^ { 4 } 2 x ^ { 19 } y ^ { - 6 }$$

Evaluate

$$32y^{6}x^{11}$$

Solution Steps

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

$$2^{4}\left(x^{-2}\right)^{4}\left(y^{3}\right)^{4}\times 2x^{19}y^{-6}$$

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

$$2^{4}x^{-8}\left(y^{3}\right)^{4}\times 2x^{19}y^{-6}$$

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

$$2^{4}x^{-8}y^{12}\times 2x^{19}y^{-6}$$

Calculate 2 to the power of 4 and get 16.

$$16x^{-8}y^{12}\times 2x^{19}y^{-6}$$

Multiply 16 and 2 to get 32.

$$32x^{-8}y^{12}x^{19}y^{-6}$$

To multiply powers of the same base, add their exponents. Add -8 and 19 to get 11.

$$32x^{11}y^{12}y^{-6}$$

To multiply powers of the same base, add their exponents. Add 12 and -6 to get 6.

$$32x^{11}y^{6}$$

Expand

$$32y^{6}x^{11}$$

Solution Steps

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

$$2^{4}\left(x^{-2}\right)^{4}\left(y^{3}\right)^{4}\times 2x^{19}y^{-6}$$

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

$$2^{4}x^{-8}\left(y^{3}\right)^{4}\times 2x^{19}y^{-6}$$

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

$$2^{4}x^{-8}y^{12}\times 2x^{19}y^{-6}$$

Calculate 2 to the power of 4 and get 16.

$$16x^{-8}y^{12}\times 2x^{19}y^{-6}$$

Multiply 16 and 2 to get 32.

$$32x^{-8}y^{12}x^{19}y^{-6}$$

To multiply powers of the same base, add their exponents. Add -8 and 19 to get 11.

$$32x^{11}y^{12}y^{-6}$$

To multiply powers of the same base, add their exponents. Add 12 and -6 to get 6.

$$32x^{11}y^{6}$$