Solve (-1/3a^2)^-4=

$$( - \frac { 1 } { 3 a ^ { 2 } } ) ^ { - 4 } =$$

Evaluate

$$81a^{8}$$

Solution Steps

Expand \left(-\frac{1}{3a^{2}}\right)^{-4}.

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

Calculate -1 to the power of -4 and get 1.

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

To raise \frac{1}{3a^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

Calculate 1 to the power of -4 and get 1.

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

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

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

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

$$\frac{1}{3^{-4}a^{-8}}$$

Calculate 3 to the power of -4 and get \frac{1}{81}.

$$\frac{1}{\frac{1}{81}a^{-8}}$$

Expand

$$81a^{8}$$

Solution Steps

Expand \left(-\frac{1}{3a^{2}}\right)^{-4}.

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

Calculate -1 to the power of -4 and get 1.

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

To raise \frac{1}{3a^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

Calculate 1 to the power of -4 and get 1.

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

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

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

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

$$\frac{1}{3^{-4}a^{-8}}$$

Calculate 3 to the power of -4 and get \frac{1}{81}.

$$\frac{1}{\frac{1}{81}a^{-8}}$$