Solve left(16y^3x^2right)^-2/8yx

$$\frac{ { \left(16 { y }^{ 3 } { x }^{ 2 } \right) }^{ -2 } }{ 8yx }$$

Evaluate

$$\frac{1}{2048x^{5}y^{7}}$$

Solution Steps

Expand \left(16y^{3}x^{2}\right)^{-2}.

$$\frac{16^{-2}\left(y^{3}\right)^{-2}\left(x^{2}\right)^{-2}}{8yx}$$

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

$$\frac{16^{-2}y^{-6}\left(x^{2}\right)^{-2}}{8yx}$$

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

$$\frac{16^{-2}y^{-6}x^{-4}}{8yx}$$

Calculate 16 to the power of -2 and get \frac{1}{256}.

$$\frac{\frac{1}{256}y^{-6}x^{-4}}{8yx}$$

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

$$\frac{\frac{1}{256}}{8x^{5}y^{7}}$$

Express \frac{\frac{1}{256}}{8x^{5}y^{7}} as a single fraction.

$$\frac{1}{256\times 8x^{5}y^{7}}$$

Multiply 256 and 8 to get 2048.

$$\frac{1}{2048x^{5}y^{7}}$$

Expand

$$\frac{1}{2048x^{5}y^{7}}$$

Solution Steps

Expand \left(16y^{3}x^{2}\right)^{-2}.

$$\frac{16^{-2}\left(y^{3}\right)^{-2}\left(x^{2}\right)^{-2}}{8yx}$$

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

$$\frac{16^{-2}y^{-6}\left(x^{2}\right)^{-2}}{8yx}$$

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

$$\frac{16^{-2}y^{-6}x^{-4}}{8yx}$$

Calculate 16 to the power of -2 and get \frac{1}{256}.

$$\frac{\frac{1}{256}y^{-6}x^{-4}}{8yx}$$

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

$$\frac{\frac{1}{256}}{8x^{5}y^{7}}$$

Express \frac{\frac{1}{256}}{8x^{5}y^{7}} as a single fraction.

$$\frac{1}{256\times 8x^{5}y^{7}}$$

Multiply 256 and 8 to get 2048.

$$\frac{1}{2048x^{5}y^{7}}$$