Solve (a^4b^-1/c)^2

$$( \frac { a ^ { 4 } b ^ { - 1 } } { c } ) ^ { 2 }$$

Evaluate

$$\frac{a^{8}}{\left(bc\right)^{2}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(\frac{a^{4}\times \frac{1}{b}}{c^{1}}\right)^{2}$$

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

$$\frac{\left(a^{4}\right)^{2}\times \left(\frac{1}{b}\right)^{2}}{\left(c^{1}\right)^{2}}$$

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

$$\frac{a^{4\times 2}b^{-2}}{c^{2}}$$

Multiply 4 times 2.

$$\frac{a^{8}b^{-2}}{c^{2}}$$

Expand

$$\frac{a^{8}}{\left(bc\right)^{2}}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(\frac{a^{4}\times \frac{1}{b}}{c^{1}}\right)^{2}$$

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

$$\frac{\left(a^{4}\right)^{2}\times \left(\frac{1}{b}\right)^{2}}{\left(c^{1}\right)^{2}}$$

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

$$\frac{a^{4\times 2}b^{-2}}{c^{2}}$$

Multiply 4 times 2.

$$\frac{a^{8}b^{-2}}{c^{2}}$$