Solve 17*16*15/3*2*left(2xright)^14*left(-3y^2right)^3

$$\frac{ 17 \times 16 \times 15 }{ 3 \times 2 } \times { \left(2x \right) }^{ 14 } \times { \left(-3 { y }^{ 2 } \right) }^{ 3 }$$

Evaluate

$$-300810240y^{6}x^{14}$$

Solution Steps

Cancel out 2\times 3 in both numerator and denominator.

$$5\times 8\times 17\times \left(2x\right)^{14}\left(-3y^{2}\right)^{3}$$

Multiply 5 and 8 to get 40.

$$40\times 17\times \left(2x\right)^{14}\left(-3y^{2}\right)^{3}$$

Multiply 40 and 17 to get 680.

$$680\times \left(2x\right)^{14}\left(-3y^{2}\right)^{3}$$

Expand \left(2x\right)^{14}.

$$680\times 2^{14}x^{14}\left(-3y^{2}\right)^{3}$$

Calculate 2 to the power of 14 and get 16384.

$$680\times 16384x^{14}\left(-3y^{2}\right)^{3}$$

Multiply 680 and 16384 to get 11141120.

$$11141120x^{14}\left(-3y^{2}\right)^{3}$$

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

$$11141120x^{14}\left(-3\right)^{3}\left(y^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$11141120x^{14}\left(-3\right)^{3}y^{6}$$

Calculate -3 to the power of 3 and get -27.

$$11141120x^{14}\left(-27\right)y^{6}$$

Multiply 11141120 and -27 to get -300810240.

$$-300810240x^{14}y^{6}$$

Expand

$$-300810240y^{6}x^{14}$$

Solution Steps

Cancel out 2\times 3 in both numerator and denominator.

$$5\times 8\times 17\times \left(2x\right)^{14}\left(-3y^{2}\right)^{3}$$

Multiply 5 and 8 to get 40.

$$40\times 17\times \left(2x\right)^{14}\left(-3y^{2}\right)^{3}$$

Multiply 40 and 17 to get 680.

$$680\times \left(2x\right)^{14}\left(-3y^{2}\right)^{3}$$

Expand \left(2x\right)^{14}.

$$680\times 2^{14}x^{14}\left(-3y^{2}\right)^{3}$$

Calculate 2 to the power of 14 and get 16384.

$$680\times 16384x^{14}\left(-3y^{2}\right)^{3}$$

Multiply 680 and 16384 to get 11141120.

$$11141120x^{14}\left(-3y^{2}\right)^{3}$$

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

$$11141120x^{14}\left(-3\right)^{3}\left(y^{2}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$11141120x^{14}\left(-3\right)^{3}y^{6}$$

Calculate -3 to the power of 3 and get -27.

$$11141120x^{14}\left(-27\right)y^{6}$$

Multiply 11141120 and -27 to get -300810240.

$$-300810240x^{14}y^{6}$$