Question

which expression is equivalent to \\((cd)^5\\)?

• \\(c^5 + d^5\\)
• \\(\frac{c^5}{d^5}\\)
• \\(c^5 d^5\\)
• \\(c^5 - d^5\\)

Explanation:

Identify the given expression

The given expression is:

$$ (cd)^5 $$

Apply the power of a product rule

The power of a product rule states that for any real numbers \( a \) and \( b \), and any integer \( n \):

$$ (ab)^n = a^n b^n $$

Applying this rule to the given expression:

$$ (cd)^5 = c^5 d^5 $$

Answer:

• (A) \(c^5 + d^5\)
• (B) \(\frac{c^5}{d^5}\)
• (C) \(c^5 d^5\) (Correct answer)
• (D) \(c^5 - d^5\)