Solve (3a^-4b^5)^-2

$$( 3 a ^ { - 4 } b ^ { 5 } ) ^ { - 2 }$$

Evaluate

$$\frac{a^{8}}{9b^{10}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(3a^{-4}b^{5}\right)^{-2}$$

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

$$3^{-2}\left(a^{-4}\right)^{-2}\left(b^{5}\right)^{-2}$$

Raise 3 to the power -2.

$$\frac{1}{9}\left(a^{-4}\right)^{-2}\left(b^{5}\right)^{-2}$$

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

$$\frac{1}{9}a^{-4\left(-2\right)}b^{5\left(-2\right)}$$

Multiply -4 times -2.

$$\frac{1}{9}a^{8}b^{5\left(-2\right)}$$

Multiply 5 times -2.

$$\frac{1}{9}a^{8}\times \frac{1}{b^{10}}$$

Expand

$$\frac{a^{8}}{9b^{10}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(3a^{-4}b^{5}\right)^{-2}$$

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

$$3^{-2}\left(a^{-4}\right)^{-2}\left(b^{5}\right)^{-2}$$

Raise 3 to the power -2.

$$\frac{1}{9}\left(a^{-4}\right)^{-2}\left(b^{5}\right)^{-2}$$

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

$$\frac{1}{9}a^{-4\left(-2\right)}b^{5\left(-2\right)}$$

Multiply -4 times -2.

$$\frac{1}{9}a^{8}b^{5\left(-2\right)}$$

Multiply 5 times -2.

$$\frac{1}{9}a^{8}\times \frac{1}{b^{10}}$$