Solve (-4a/3b^-3)^-2

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

Evaluate

$$\frac{9}{16a^{2}b^{6}}$$

Solution Steps

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

$$\left(-1\right)^{-2}\times \left(\frac{4a}{3b^{-3}}\right)^{-2}$$

Calculate -1 to the power of -2 and get 1.

$$1\times \left(\frac{4a}{3b^{-3}}\right)^{-2}$$

To raise \frac{4a}{3b^{-3}} to a power, raise both numerator and denominator to the power and then divide.

$$1\times \frac{\left(4a\right)^{-2}}{\left(3b^{-3}\right)^{-2}}$$

Express 1\times \frac{\left(4a\right)^{-2}}{\left(3b^{-3}\right)^{-2}} as a single fraction.

$$\frac{\left(4a\right)^{-2}}{\left(3b^{-3}\right)^{-2}}$$

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

$$\frac{4^{-2}a^{-2}}{\left(3b^{-3}\right)^{-2}}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{\frac{1}{16}a^{-2}}{\left(3b^{-3}\right)^{-2}}$$

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

$$\frac{\frac{1}{16}a^{-2}}{3^{-2}\left(b^{-3}\right)^{-2}}$$

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

$$\frac{\frac{1}{16}a^{-2}}{3^{-2}b^{6}}$$

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

$$\frac{\frac{1}{16}a^{-2}}{\frac{1}{9}b^{6}}$$

Expand

$$\frac{9}{16a^{2}b^{6}}$$

Solution Steps

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

$$\left(-1\right)^{-2}\times \left(\frac{4a}{3b^{-3}}\right)^{-2}$$

Calculate -1 to the power of -2 and get 1.

$$1\times \left(\frac{4a}{3b^{-3}}\right)^{-2}$$

To raise \frac{4a}{3b^{-3}} to a power, raise both numerator and denominator to the power and then divide.

$$1\times \frac{\left(4a\right)^{-2}}{\left(3b^{-3}\right)^{-2}}$$

Express 1\times \frac{\left(4a\right)^{-2}}{\left(3b^{-3}\right)^{-2}} as a single fraction.

$$\frac{\left(4a\right)^{-2}}{\left(3b^{-3}\right)^{-2}}$$

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

$$\frac{4^{-2}a^{-2}}{\left(3b^{-3}\right)^{-2}}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{\frac{1}{16}a^{-2}}{\left(3b^{-3}\right)^{-2}}$$

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

$$\frac{\frac{1}{16}a^{-2}}{3^{-2}\left(b^{-3}\right)^{-2}}$$

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

$$\frac{\frac{1}{16}a^{-2}}{3^{-2}b^{6}}$$

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

$$\frac{\frac{1}{16}a^{-2}}{\frac{1}{9}b^{6}}$$