Solve (a^-2c^0/b^3)^-2

$$( \frac { a ^ { - 2 } c ^ { 0 } } { b ^ { 3 } } ) ^ { - 2 }$$

Evaluate

$$a^{4}b^{6}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(\frac{a^{-2}c^{0}}{b^{3}}\right)^{-2}$$

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

$$\frac{\left(a^{-2}\right)^{-2}\left(c^{0}\right)^{-2}}{\left(b^{3}\right)^{-2}}$$

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

$$\frac{a^{-2\left(-2\right)}c^{0}}{b^{3\left(-2\right)}}$$

Multiply -2 times -2.

$$\frac{a^{4}c^{0}}{b^{3\left(-2\right)}}$$

Multiply 3 times -2.

$$\frac{a^{4}c^{0}}{b^{-6}}$$

For any number a except 0, a^{0}=1.

$$\frac{a^{4}b^{6}}{1}$$

Expand

$$a^{4}b^{6}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(\frac{a^{-2}c^{0}}{b^{3}}\right)^{-2}$$

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

$$\frac{\left(a^{-2}\right)^{-2}\left(c^{0}\right)^{-2}}{\left(b^{3}\right)^{-2}}$$

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

$$\frac{a^{-2\left(-2\right)}c^{0}}{b^{3\left(-2\right)}}$$

Multiply -2 times -2.

$$\frac{a^{4}c^{0}}{b^{3\left(-2\right)}}$$

Multiply 3 times -2.

$$\frac{a^{4}c^{0}}{b^{-6}}$$

For any number a except 0, a^{0}=1.

$$\frac{a^{4}b^{6}}{1}$$