Solve -4(3a^-1b^4)^-2

$$- 4 ( 3 a ^ { - 1 } b ^ { 4 } ) ^ { - 2 }$$

Evaluate

$$-\frac{4a^{2}}{9b^{8}}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply -1 and -2 to get 2.

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

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

$$-4\times 3^{-2}a^{2}b^{-8}$$

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

$$-4\times \frac{1}{9}a^{2}b^{-8}$$

Multiply -4 and \frac{1}{9} to get -\frac{4}{9}.

$$-\frac{4}{9}a^{2}b^{-8}$$

Expand

$$-\frac{4a^{2}}{9b^{8}}$$

Solution Steps

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

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

To raise a power to another power, multiply the exponents. Multiply -1 and -2 to get 2.

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

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

$$-4\times 3^{-2}a^{2}b^{-8}$$

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

$$-4\times \frac{1}{9}a^{2}b^{-8}$$

Multiply -4 and \frac{1}{9} to get -\frac{4}{9}.

$$-\frac{4}{9}a^{2}b^{-8}$$