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

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

Evaluate

$$\frac{b^{6}}{4\left(ac\right)^{8}}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

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

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

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

Raise 2 to the power -2.

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

To raise a power to another power, multiply the exponents.

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

Multiply 4 times -2.

$$\frac{1}{4}\times \frac{1}{a^{8}}b^{-3\left(-2\right)}c^{4\left(-2\right)}$$

Multiply -3 times -2.

$$\frac{1}{4}\times \frac{1}{a^{8}}b^{6}c^{4\left(-2\right)}$$

Multiply 4 times -2.

$$\frac{1}{4}\times \frac{1}{a^{8}}b^{6}\times \frac{1}{c^{8}}$$

Expand

$$\frac{b^{6}}{4\left(ac\right)^{8}}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

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

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

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

Raise 2 to the power -2.

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

To raise a power to another power, multiply the exponents.

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

Multiply 4 times -2.

$$\frac{1}{4}\times \frac{1}{a^{8}}b^{-3\left(-2\right)}c^{4\left(-2\right)}$$

Multiply -3 times -2.

$$\frac{1}{4}\times \frac{1}{a^{8}}b^{6}c^{4\left(-2\right)}$$

Multiply 4 times -2.

$$\frac{1}{4}\times \frac{1}{a^{8}}b^{6}\times \frac{1}{c^{8}}$$