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

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

Evaluate

$$\frac{b^{6}}{64a^{15}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 4 to the power -3.

$$\frac{1}{64}\left(a^{5}\right)^{-3}\left(b^{-2}\right)^{-3}$$

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

$$\frac{1}{64}a^{5\left(-3\right)}b^{-2\left(-3\right)}$$

Multiply 5 times -3.

$$\frac{1}{64}\times \frac{1}{a^{15}}b^{-2\left(-3\right)}$$

Multiply -2 times -3.

$$\frac{1}{64}\times \frac{1}{a^{15}}b^{6}$$

Expand

$$\frac{b^{6}}{64a^{15}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

Raise 4 to the power -3.

$$\frac{1}{64}\left(a^{5}\right)^{-3}\left(b^{-2}\right)^{-3}$$

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

$$\frac{1}{64}a^{5\left(-3\right)}b^{-2\left(-3\right)}$$

Multiply 5 times -3.

$$\frac{1}{64}\times \frac{1}{a^{15}}b^{-2\left(-3\right)}$$

Multiply -2 times -3.

$$\frac{1}{64}\times \frac{1}{a^{15}}b^{6}$$