Solve left(3a^2b^-2ca^-1right)^2

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

Evaluate

$$\frac{9\left(ac\right)^{2}}{b^{4}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and -1 to get 1.

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

Calculate a to the power of 1 and get a.

$$\left(3ab^{-2}c\right)^{2}$$

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

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

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

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

Calculate 3 to the power of 2 and get 9.

$$9a^{2}b^{-4}c^{2}$$

Expand

$$\frac{9\left(ac\right)^{2}}{b^{4}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and -1 to get 1.

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

Calculate a to the power of 1 and get a.

$$\left(3ab^{-2}c\right)^{2}$$

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

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

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

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

Calculate 3 to the power of 2 and get 9.

$$9a^{2}b^{-4}c^{2}$$