Complete the Expression: Finding (15)^xy Power with Multiple Variables

Question

Insert the corresponding expression:

(15)xy= \left(15\right)^{xy}=

Video Solution

Step-by-Step Solution

To solve this problem, we will rewrite the expression (15)xy (15)^{xy} using the rules of exponents.

  • Step 1: Understand that (15)xy (15)^{xy} can be rewritten using the power of a power rule.
  • Step 2: Apply the exponent rule (am)n=am×n(a^m)^n = a^{m \times n}. We know (15x)y=(15)x×y(15^x)^y = (15)^{x \times y} and (15y)x=(15)y×x(15^y)^x = (15)^{y \times x}, both equivalent to (15)xy (15)^{xy} .
  • Step 3: Analyze each choice:

Choice 1: (15y)x (15^y)^x is equivalent to (15)xy(15)^{xy} since applying the rule gives us (15y)x=(15)y×x=(15)xy(15^y)^x = (15)^{y \times x} = (15)^{xy}.
Choice 2: (15x)y (15^x)^y is also equivalent to (15)xy(15)^{xy} because applying the rule provides (15x)y=(15)x×y=(15)xy(15^x)^y = (15)^{x \times y} = (15)^{xy}.
Choice 3: 15x×15y 15^x \times 15^y results in 15x+y15^{x+y}, which is not equivalent to (15)xy(15)^{xy} as it uses the product of powers rule.\
Choice 4: Both (15y)x (15^y)^x and (15x)y (15^x)^y are correct based on the rules involved.

Based on the analysis, choice 4 (a'+b' are correct) is the correct answer.
Both (15y)x(15^y)^x and (15x)y(15^x)^y are equivalent representations of (15)xy (15)^{xy}.

Answer

a'+b' are correct