Solve (4x^3y^4)^3/5^-2xy=

$$\frac { ( 4 x ^ { 3 } y ^ { 4 } ) ^ { 3 } } { 5 ^ { - 2 } x y } =$$

Evaluate

$$1600x^{8}y^{11}$$

Solution Steps

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

$$\frac{4^{3}\left(x^{3}\right)^{3}\left(y^{4}\right)^{3}}{5^{-2}xy}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{4^{3}x^{9}\left(y^{4}\right)^{3}}{5^{-2}xy}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{4^{3}x^{9}y^{12}}{5^{-2}xy}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64x^{9}y^{12}}{5^{-2}xy}$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{64x^{9}y^{12}}{\frac{1}{25}xy}$$

Cancel out xy in both numerator and denominator.

$$\frac{64x^{8}y^{11}}{\frac{1}{25}}$$

Divide 64x^{8}y^{11} by \frac{1}{25} by multiplying 64x^{8}y^{11} by the reciprocal of \frac{1}{25}.

$$64x^{8}y^{11}\times 25$$

Multiply 64 and 25 to get 1600.

$$1600x^{8}y^{11}$$

Expand

$$1600x^{8}y^{11}$$

Solution Steps

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

$$\frac{4^{3}\left(x^{3}\right)^{3}\left(y^{4}\right)^{3}}{5^{-2}xy}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{4^{3}x^{9}\left(y^{4}\right)^{3}}{5^{-2}xy}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{4^{3}x^{9}y^{12}}{5^{-2}xy}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64x^{9}y^{12}}{5^{-2}xy}$$

Calculate 5 to the power of -2 and get \frac{1}{25}.

$$\frac{64x^{9}y^{12}}{\frac{1}{25}xy}$$

Cancel out xy in both numerator and denominator.

$$\frac{64x^{8}y^{11}}{\frac{1}{25}}$$

Divide 64x^{8}y^{11} by \frac{1}{25} by multiplying 64x^{8}y^{11} by the reciprocal of \frac{1}{25}.

$$64x^{8}y^{11}\times 25$$

Multiply 64 and 25 to get 1600.

$$1600x^{8}y^{11}$$