Solve (3a^3bc^-5)^-4

$$( 3 a ^ { 3 } b c ^ { - 5 } ) ^ { - 4 }$$

Evaluate

$$\frac{c^{20}}{81b^{4}a^{12}}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(3a^{3}b^{1}c^{-5}\right)^{-4}$$

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

$$3^{-4}\left(a^{3}\right)^{-4}\left(b^{1}\right)^{-4}\left(c^{-5}\right)^{-4}$$

Raise 3 to the power -4.

$$\frac{1}{81}\left(a^{3}\right)^{-4}\left(b^{1}\right)^{-4}\left(c^{-5}\right)^{-4}$$

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

$$\frac{1}{81}a^{3\left(-4\right)}b^{-4}c^{-5\left(-4\right)}$$

Multiply 3 times -4.

$$\frac{1}{81}\times \frac{1}{a^{12}}b^{-4}c^{-5\left(-4\right)}$$

Multiply -5 times -4.

$$\frac{1}{81}\times \frac{1}{a^{12}}\times \frac{1}{b^{4}}c^{20}$$

Expand

$$\frac{c^{20}}{81b^{4}a^{12}}$$

Steps for Raising Product to a Power

Use the rules of exponents to simplify the expression.

$$\left(3a^{3}b^{1}c^{-5}\right)^{-4}$$

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

$$3^{-4}\left(a^{3}\right)^{-4}\left(b^{1}\right)^{-4}\left(c^{-5}\right)^{-4}$$

Raise 3 to the power -4.

$$\frac{1}{81}\left(a^{3}\right)^{-4}\left(b^{1}\right)^{-4}\left(c^{-5}\right)^{-4}$$

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

$$\frac{1}{81}a^{3\left(-4\right)}b^{-4}c^{-5\left(-4\right)}$$

Multiply 3 times -4.

$$\frac{1}{81}\times \frac{1}{a^{12}}b^{-4}c^{-5\left(-4\right)}$$

Multiply -5 times -4.

$$\frac{1}{81}\times \frac{1}{a^{12}}\times \frac{1}{b^{4}}c^{20}$$