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

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

Evaluate

$$\frac{b^{16}}{16a^{20}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 2 to the power -4.

$$\frac{1}{16}\left(a^{5}\right)^{-4}\left(b^{-4}\right)^{-4}$$

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

$$\frac{1}{16}a^{5\left(-4\right)}b^{-4\left(-4\right)}$$

Multiply 5 times -4.

$$\frac{1}{16}\times \frac{1}{a^{20}}b^{-4\left(-4\right)}$$

Multiply -4 times -4.

$$\frac{1}{16}\times \frac{1}{a^{20}}b^{16}$$

Expand

$$\frac{b^{16}}{16a^{20}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 2 to the power -4.

$$\frac{1}{16}\left(a^{5}\right)^{-4}\left(b^{-4}\right)^{-4}$$

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

$$\frac{1}{16}a^{5\left(-4\right)}b^{-4\left(-4\right)}$$

Multiply 5 times -4.

$$\frac{1}{16}\times \frac{1}{a^{20}}b^{-4\left(-4\right)}$$

Multiply -4 times -4.

$$\frac{1}{16}\times \frac{1}{a^{20}}b^{16}$$