Solve (a^2/b)^-3

$$( \frac { a ^ { 2 } } { b } ) ^ { - 3 }$$

Evaluate

$$\frac{b^{3}}{a^{6}}$$

Steps for Raising the Quotient to a Power

Use the rules of exponents to simplify the expression.

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

To raise the quotient of two numbers to a power, raise each number to the power and then divide.

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

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

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

Multiply 2 times -3.

$$\frac{a^{-6}}{b^{-3}}$$

Multiply 1 times -3.

$$\frac{1}{a^{6}b^{-3}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

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

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

Multiply 2 times -3.

$$\frac{1}{a^{6}}b^{-\left(-3\right)}$$

Multiply -1 times -3.

$$\frac{1}{a^{6}}b^{3}$$

Expand

$$\frac{b^{3}}{a^{6}}$$

Steps for Raising the Quotient to a Power

Use the rules of exponents to simplify the expression.

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

To raise the quotient of two numbers to a power, raise each number to the power and then divide.

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

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

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

Multiply 2 times -3.

$$\frac{a^{-6}}{b^{-3}}$$

Multiply 1 times -3.

$$\frac{1}{a^{6}b^{-3}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

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

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

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

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

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

Multiply 2 times -3.

$$\frac{1}{a^{6}}b^{-\left(-3\right)}$$

Multiply -1 times -3.

$$\frac{1}{a^{6}}b^{3}$$