Solve (a^-2b^-1)^3=

$$( a ^ { - 2 } b ^ { - 1 } ) ^ { 3 } =$$

Evaluate

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

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.

$$\frac{a^{-2\times 3}}{b^{3}}$$

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.

$$a^{-2\times 3}b^{-3}$$

Multiply -2 times 3.

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

Multiply -1 times 3.

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

Expand

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

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.

$$\frac{a^{-2\times 3}}{b^{3}}$$

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.

$$a^{-2\times 3}b^{-3}$$

Multiply -2 times 3.

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

Multiply -1 times 3.

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