Solve 4xyquad8x^{2}y^{3}quad8x^3y^4quadquad32x^2y^3

$$4 x y \quad 8 x ^ { 2 } y ^ { 3 } \quad 8 x ^ { 3 } y ^ { 4 } \quad \quad 32 x ^ { 2 } y ^ { 3 }$$

Evaluate

$$1024y_{8}x^{8}y^{10}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$4x^{3}y_{8}y^{3}\times 8x^{3}y^{4}\times 32x^{2}y^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$4x^{6}y_{8}y^{3}\times 8y^{4}\times 32x^{2}y^{3}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$4x^{8}y_{8}y^{3}\times 8y^{4}\times 32y^{3}$$

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$4x^{8}y_{8}y^{7}\times 8\times 32y^{3}$$

To multiply powers of the same base, add their exponents. Add 7 and 3 to get 10.

$$4x^{8}y_{8}y^{10}\times 8\times 32$$

Multiply 4 and 8 to get 32.

$$32x^{8}y_{8}y^{10}\times 32$$

Multiply 32 and 32 to get 1024.

$$1024x^{8}y_{8}y^{10}$$

Differentiate w.r.t. x

$$8192y_{8}x^{7}y^{10}$$