Full solution

Q. Evaluate. Write your answer as a fraction or whole number.

\newline

(\frac{1}{4})^4

= _____

Identify base and exponent: Identify the base and the exponent in the expression $\left(\frac{1}{4}\right)^4$ . $\newline$ Base: $\frac{1}{4}$ $\newline$ Exponent: $4$
Understanding exponentiation of fractions: Understand that raising a fraction to an exponent means multiplying the fraction by itself as many times as the value of the exponent. $(\frac{1}{4})^4$ means $\frac{1}{4}$ multiplied by itself $4$ times.
Write expanded form: Write the expanded form of $\left(\frac{1}{4}\right)^4$ . $\newline$ Expanded Form: $\frac{1}{4} \times \frac{1}{4} \times \frac{1}{4} \times \frac{1}{4}$
Multiply numerators and denominators: Multiply the numerators and the denominators separately. $\newline$ $\left(\frac{1}{4}\right)^4 = \frac{1 \times 1 \times 1 \times 1}{4 \times 4 \times 4 \times 4}$
Calculate product of numerators and denominators: Calculate the product of the numerators and the product of the denominators. $\newline$ $1 \times 1 \times 1 \times 1 = 1$ $\newline$ $4 \times 4 \times 4 \times 4 = 256$
Combine products for final answer: Combine the products to get the final answer. $\newline$ $\left(\frac{1}{4}\right)^4 = \frac{1}{256}$