Solve y(3b^-4g^3)^-2/(4b)^2

$$y \frac { ( 3 b ^ { - 4 } g ^ { 3 } ) ^ { - 2 } } { ( 4 b ) ^ { 2 } }$$

Evaluate

$$\frac{\left(\frac{b}{g}\right)^{6}y}{144}$$

Solution Steps

Expand \left(3b^{-4}g^{3}\right)^{-2}.

$$y\times \frac{3^{-2}\left(b^{-4}\right)^{-2}\left(g^{3}\right)^{-2}}{\left(4b\right)^{2}}$$

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

$$y\times \frac{3^{-2}b^{8}\left(g^{3}\right)^{-2}}{\left(4b\right)^{2}}$$

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

$$y\times \frac{3^{-2}b^{8}g^{-6}}{\left(4b\right)^{2}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$y\times \frac{\frac{1}{9}b^{8}g^{-6}}{\left(4b\right)^{2}}$$

Expand \left(4b\right)^{2}.

$$y\times \frac{\frac{1}{9}b^{8}g^{-6}}{4^{2}b^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$y\times \frac{\frac{1}{9}b^{8}g^{-6}}{16b^{2}}$$

Cancel out b^{2} in both numerator and denominator.

$$y\times \frac{\frac{1}{9}g^{-6}b^{6}}{16}$$

Divide \frac{1}{9}g^{-6}b^{6} by 16 to get \frac{1}{144}g^{-6}b^{6}.

$$y\times \frac{1}{144}g^{-6}b^{6}$$

Expand

$$\frac{\left(\frac{b}{g}\right)^{6}y}{144}$$

Solution Steps

Expand \left(3b^{-4}g^{3}\right)^{-2}.

$$y\times \frac{3^{-2}\left(b^{-4}\right)^{-2}\left(g^{3}\right)^{-2}}{\left(4b\right)^{2}}$$

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

$$y\times \frac{3^{-2}b^{8}\left(g^{3}\right)^{-2}}{\left(4b\right)^{2}}$$

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

$$y\times \frac{3^{-2}b^{8}g^{-6}}{\left(4b\right)^{2}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$y\times \frac{\frac{1}{9}b^{8}g^{-6}}{\left(4b\right)^{2}}$$

Expand \left(4b\right)^{2}.

$$y\times \frac{\frac{1}{9}b^{8}g^{-6}}{4^{2}b^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$y\times \frac{\frac{1}{9}b^{8}g^{-6}}{16b^{2}}$$

Cancel out b^{2} in both numerator and denominator.

$$y\times \frac{\frac{1}{9}g^{-6}b^{6}}{16}$$

Divide \frac{1}{9}g^{-6}b^{6} by 16 to get \frac{1}{144}g^{-6}b^{6}.

$$y\times \frac{1}{144}g^{-6}b^{6}$$