Solve 3x^5y(4xy^7)^3

$$3 x ^ { 5 } y ( 4 x y ^ { 7 } ) ^ { 3 }$$

Evaluate

$$192x^{8}y^{22}$$

Solution Steps

Expand \left(4xy^{7}\right)^{3}.

$$3x^{5}y\times 4^{3}x^{3}\left(y^{7}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$3x^{5}y\times 4^{3}x^{3}y^{21}$$

Calculate 4 to the power of 3 and get 64.

$$3x^{5}y\times 64x^{3}y^{21}$$

Multiply 3 and 64 to get 192.

$$192x^{5}yx^{3}y^{21}$$

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$192x^{8}yy^{21}$$

To multiply powers of the same base, add their exponents. Add 1 and 21 to get 22.

$$192x^{8}y^{22}$$

Expand

$$192x^{8}y^{22}$$

Solution Steps

Expand \left(4xy^{7}\right)^{3}.

$$3x^{5}y\times 4^{3}x^{3}\left(y^{7}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 3 to get 21.

$$3x^{5}y\times 4^{3}x^{3}y^{21}$$

Calculate 4 to the power of 3 and get 64.

$$3x^{5}y\times 64x^{3}y^{21}$$

Multiply 3 and 64 to get 192.

$$192x^{5}yx^{3}y^{21}$$

To multiply powers of the same base, add their exponents. Add 5 and 3 to get 8.

$$192x^{8}yy^{21}$$

To multiply powers of the same base, add their exponents. Add 1 and 21 to get 22.

$$192x^{8}y^{22}$$