Solve (1/4ad^3)^2

$$( \frac { 1 } { 4 } a d ^ { 3 } ) ^ { 2 }$$

Evaluate

$$\frac{a^{2}d^{6}}{16}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(\frac{1}{4}a^{1}d^{3}\right)^{2}$$

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

$$\left(\frac{1}{4}\right)^{2}\left(a^{1}\right)^{2}\left(d^{3}\right)^{2}$$

Raise \frac{1}{4} to the power 2.

$$\frac{1}{16}\left(a^{1}\right)^{2}\left(d^{3}\right)^{2}$$

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

$$\frac{1}{16}a^{2}d^{3\times 2}$$

Multiply 3 times 2.

$$\frac{1}{16}a^{2}d^{6}$$

Expand

$$\frac{a^{2}d^{6}}{16}$$

Solution Steps

Use the rules of exponents to simplify the expression.

$$\left(\frac{1}{4}a^{1}d^{3}\right)^{2}$$

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

$$\left(\frac{1}{4}\right)^{2}\left(a^{1}\right)^{2}\left(d^{3}\right)^{2}$$

Raise \frac{1}{4} to the power 2.

$$\frac{1}{16}\left(a^{1}\right)^{2}\left(d^{3}\right)^{2}$$

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

$$\frac{1}{16}a^{2}d^{3\times 2}$$

Multiply 3 times 2.

$$\frac{1}{16}a^{2}d^{6}$$