Solve (8x^3y^4)^-2/4xy

$$\frac { ( 8 x ^ { 3 } y ^ { 4 } ) ^ { - 2 } } { 4 x y }$$

Evaluate

$$\frac{1}{256x^{7}y^{9}}$$

Solution Steps

Expand \left(8x^{3}y^{4}\right)^{-2}.

$$\frac{8^{-2}\left(x^{3}\right)^{-2}\left(y^{4}\right)^{-2}}{4xy}$$

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

$$\frac{8^{-2}x^{-6}\left(y^{4}\right)^{-2}}{4xy}$$

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

$$\frac{8^{-2}x^{-6}y^{-8}}{4xy}$$

Calculate 8 to the power of -2 and get \frac{1}{64}.

$$\frac{\frac{1}{64}x^{-6}y^{-8}}{4xy}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{\frac{1}{64}}{4x^{7}y^{9}}$$

Express \frac{\frac{1}{64}}{4x^{7}y^{9}} as a single fraction.

$$\frac{1}{64\times 4x^{7}y^{9}}$$

Multiply 64 and 4 to get 256.

$$\frac{1}{256x^{7}y^{9}}$$

Expand

$$\frac{1}{256x^{7}y^{9}}$$

Solution Steps

Expand \left(8x^{3}y^{4}\right)^{-2}.

$$\frac{8^{-2}\left(x^{3}\right)^{-2}\left(y^{4}\right)^{-2}}{4xy}$$

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

$$\frac{8^{-2}x^{-6}\left(y^{4}\right)^{-2}}{4xy}$$

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

$$\frac{8^{-2}x^{-6}y^{-8}}{4xy}$$

Calculate 8 to the power of -2 and get \frac{1}{64}.

$$\frac{\frac{1}{64}x^{-6}y^{-8}}{4xy}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{\frac{1}{64}}{4x^{7}y^{9}}$$

Express \frac{\frac{1}{64}}{4x^{7}y^{9}} as a single fraction.

$$\frac{1}{64\times 4x^{7}y^{9}}$$

Multiply 64 and 4 to get 256.

$$\frac{1}{256x^{7}y^{9}}$$