Solve 7(4xy^5)^2(xy)^4

$$7 ( 4 x y ^ { 5 } ) ^ { 2 } ( x y ) ^ { 4 }$$

Evaluate

$$112x^{6}y^{14}$$

Solution Steps

Expand \left(4xy^{5}\right)^{2}.

$$7\times 4^{2}x^{2}\left(y^{5}\right)^{2}\left(xy\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$7\times 4^{2}x^{2}y^{10}\left(xy\right)^{4}$$

Calculate 4 to the power of 2 and get 16.

$$7\times 16x^{2}y^{10}\left(xy\right)^{4}$$

Multiply 7 and 16 to get 112.

$$112x^{2}y^{10}\left(xy\right)^{4}$$

Expand \left(xy\right)^{4}.

$$112x^{2}y^{10}x^{4}y^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$112x^{6}y^{10}y^{4}$$

To multiply powers of the same base, add their exponents. Add 10 and 4 to get 14.

$$112x^{6}y^{14}$$

Expand

$$112x^{6}y^{14}$$

Solution Steps

Expand \left(4xy^{5}\right)^{2}.

$$7\times 4^{2}x^{2}\left(y^{5}\right)^{2}\left(xy\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$7\times 4^{2}x^{2}y^{10}\left(xy\right)^{4}$$

Calculate 4 to the power of 2 and get 16.

$$7\times 16x^{2}y^{10}\left(xy\right)^{4}$$

Multiply 7 and 16 to get 112.

$$112x^{2}y^{10}\left(xy\right)^{4}$$

Expand \left(xy\right)^{4}.

$$112x^{2}y^{10}x^{4}y^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$112x^{6}y^{10}y^{4}$$

To multiply powers of the same base, add their exponents. Add 10 and 4 to get 14.

$$112x^{6}y^{14}$$