Solve (3ab^-3)^-2

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

Evaluate

$$\frac{b^{6}}{9a^{2}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 3 to the power -2.

$$\frac{1}{9}\left(a^{1}\right)^{-2}\left(b^{-3}\right)^{-2}$$

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

$$\frac{1}{9}a^{-2}b^{-3\left(-2\right)}$$

Multiply -3 times -2.

$$\frac{1}{9}\times \frac{1}{a^{2}}b^{6}$$

Expand

$$\frac{b^{6}}{9a^{2}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 3 to the power -2.

$$\frac{1}{9}\left(a^{1}\right)^{-2}\left(b^{-3}\right)^{-2}$$

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

$$\frac{1}{9}a^{-2}b^{-3\left(-2\right)}$$

Multiply -3 times -2.

$$\frac{1}{9}\times \frac{1}{a^{2}}b^{6}$$