Solve left(2a^6b^-4right)^-5

$${ \left(2 { a }^{ 6 } { b }^{ -4 } \right) }^{ -5 }$$

Evaluate

$$\frac{b^{20}}{32a^{30}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(2a^{6}b^{-4}\right)^{-5}$$

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

$$2^{-5}\left(a^{6}\right)^{-5}\left(b^{-4}\right)^{-5}$$

Raise 2 to the power -5.

$$\frac{1}{32}\left(a^{6}\right)^{-5}\left(b^{-4}\right)^{-5}$$

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

$$\frac{1}{32}a^{6\left(-5\right)}b^{-4\left(-5\right)}$$

Multiply 6 times -5.

$$\frac{1}{32}\times \frac{1}{a^{30}}b^{-4\left(-5\right)}$$

Multiply -4 times -5.

$$\frac{1}{32}\times \frac{1}{a^{30}}b^{20}$$

Expand

$$\frac{b^{20}}{32a^{30}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(2a^{6}b^{-4}\right)^{-5}$$

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

$$2^{-5}\left(a^{6}\right)^{-5}\left(b^{-4}\right)^{-5}$$

Raise 2 to the power -5.

$$\frac{1}{32}\left(a^{6}\right)^{-5}\left(b^{-4}\right)^{-5}$$

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

$$\frac{1}{32}a^{6\left(-5\right)}b^{-4\left(-5\right)}$$

Multiply 6 times -5.

$$\frac{1}{32}\times \frac{1}{a^{30}}b^{-4\left(-5\right)}$$

Multiply -4 times -5.

$$\frac{1}{32}\times \frac{1}{a^{30}}b^{20}$$