Solve (5x^{2}y^3)(3x^2y^5)^4

$$( 5 x ^ { 2 } y ^ { 3 } ) ( 3 x ^ { 2 } y ^ { 5 } ) ^ { 4 }$$

Evaluate

$$405x^{10}y^{23}$$

Solution Steps

Expand \left(3x^{2}y^{5}\right)^{4}.

$$5x^{2}y^{3}\times 3^{4}\left(x^{2}\right)^{4}\left(y^{5}\right)^{4}$$

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

$$5x^{2}y^{3}\times 3^{4}x^{8}\left(y^{5}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$5x^{2}y^{3}\times 3^{4}x^{8}y^{20}$$

Calculate 3 to the power of 4 and get 81.

$$5x^{2}y^{3}\times 81x^{8}y^{20}$$

Multiply 5 and 81 to get 405.

$$405x^{2}y^{3}x^{8}y^{20}$$

To multiply powers of the same base, add their exponents. Add 2 and 8 to get 10.

$$405x^{10}y^{3}y^{20}$$

To multiply powers of the same base, add their exponents. Add 3 and 20 to get 23.

$$405x^{10}y^{23}$$

Expand

$$405x^{10}y^{23}$$

Solution Steps

Expand \left(3x^{2}y^{5}\right)^{4}.

$$5x^{2}y^{3}\times 3^{4}\left(x^{2}\right)^{4}\left(y^{5}\right)^{4}$$

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

$$5x^{2}y^{3}\times 3^{4}x^{8}\left(y^{5}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$5x^{2}y^{3}\times 3^{4}x^{8}y^{20}$$

Calculate 3 to the power of 4 and get 81.

$$5x^{2}y^{3}\times 81x^{8}y^{20}$$

Multiply 5 and 81 to get 405.

$$405x^{2}y^{3}x^{8}y^{20}$$

To multiply powers of the same base, add their exponents. Add 2 and 8 to get 10.

$$405x^{10}y^{3}y^{20}$$

To multiply powers of the same base, add their exponents. Add 3 and 20 to get 23.

$$405x^{10}y^{23}$$