Simplify.
${\left(\frac{y^4}{5}\right)}^3$

• A. $\frac{y^{64}}{125}$
• B. $\(\frac{y^{12}\)}{125}$
• C. $\(\frac{y^{12}\)}{5}$
• D. $\(\frac{y^4}{125}\)$

Answer: (B)

Verified step by step guidance

1. Identify the expression to simplify: \(\left(\frac{y^4}{5}\right)^3\).
2. Apply the power of a quotient rule, which states that \(\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}\). So rewrite the expression as \(\frac{(y^4)^3}{5^3}\).
3. Use the power of a power rule for the numerator: \((y^4)^3 = y^{4 \times 3} = y^{12}\).
4. Calculate the denominator by raising 5 to the power of 3: \$5^3 = 125$.
5. Combine the results to write the simplified expression as \(\frac{y^{12}}{125}\).