Solve (5q^3b^-3)^-3

$$( 5 q ^ { 3 } b ^ { - 3 } ) ^ { - 3 }$$

Evaluate

$$\frac{\left(\frac{b}{q}\right)^{9}}{125}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(5q^{3}b^{-3}\right)^{-3}$$

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

$$5^{-3}\left(q^{3}\right)^{-3}\left(b^{-3}\right)^{-3}$$

Raise 5 to the power -3.

$$\frac{1}{125}\left(q^{3}\right)^{-3}\left(b^{-3}\right)^{-3}$$

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

$$\frac{1}{125}q^{3\left(-3\right)}b^{-3\left(-3\right)}$$

Multiply 3 times -3.

$$\frac{1}{125}\times \frac{1}{q^{9}}b^{-3\left(-3\right)}$$

Multiply -3 times -3.

$$\frac{1}{125}\times \frac{1}{q^{9}}b^{9}$$

Expand

$$\frac{\left(\frac{b}{q}\right)^{9}}{125}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(5q^{3}b^{-3}\right)^{-3}$$

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

$$5^{-3}\left(q^{3}\right)^{-3}\left(b^{-3}\right)^{-3}$$

Raise 5 to the power -3.

$$\frac{1}{125}\left(q^{3}\right)^{-3}\left(b^{-3}\right)^{-3}$$

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

$$\frac{1}{125}q^{3\left(-3\right)}b^{-3\left(-3\right)}$$

Multiply 3 times -3.

$$\frac{1}{125}\times \frac{1}{q^{9}}b^{-3\left(-3\right)}$$

Multiply -3 times -3.

$$\frac{1}{125}\times \frac{1}{q^{9}}b^{9}$$