Solve (4a^-6b^4)^-2

$$( 4 a ^ { - 6 } b ^ { 4 } ) ^ { - 2 }$$

Evaluate

$$\frac{a^{12}}{16b^{8}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(4a^{-6}b^{4}\right)^{-2}$$

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

$$4^{-2}\left(a^{-6}\right)^{-2}\left(b^{4}\right)^{-2}$$

Raise 4 to the power -2.

$$\frac{1}{16}\left(a^{-6}\right)^{-2}\left(b^{4}\right)^{-2}$$

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

$$\frac{1}{16}a^{-6\left(-2\right)}b^{4\left(-2\right)}$$

Multiply -6 times -2.

$$\frac{1}{16}a^{12}b^{4\left(-2\right)}$$

Multiply 4 times -2.

$$\frac{1}{16}a^{12}\times \frac{1}{b^{8}}$$

Expand

$$\frac{a^{12}}{16b^{8}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(4a^{-6}b^{4}\right)^{-2}$$

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

$$4^{-2}\left(a^{-6}\right)^{-2}\left(b^{4}\right)^{-2}$$

Raise 4 to the power -2.

$$\frac{1}{16}\left(a^{-6}\right)^{-2}\left(b^{4}\right)^{-2}$$

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

$$\frac{1}{16}a^{-6\left(-2\right)}b^{4\left(-2\right)}$$

Multiply -6 times -2.

$$\frac{1}{16}a^{12}b^{4\left(-2\right)}$$

Multiply 4 times -2.

$$\frac{1}{16}a^{12}\times \frac{1}{b^{8}}$$