Insert the corresponding expression:
(15)xy=
To solve this problem, we will rewrite the expression (15)xy using the rules of exponents.
- Step 1: Understand that (15)xy can be rewritten using the power of a power rule.
- Step 2: Apply the exponent rule (am)n=am×n. We know (15x)y=(15)x×y and (15y)x=(15)y×x, both equivalent to (15)xy.
- Step 3: Analyze each choice:
Choice 1: (15y)x is equivalent to (15)xy since applying the rule gives us (15y)x=(15)y×x=(15)xy.
Choice 2: (15x)y is also equivalent to (15)xy because applying the rule provides (15x)y=(15)x×y=(15)xy.
Choice 3: 15x×15y results in 15x+y, which is not equivalent to (15)xy as it uses the product of powers rule.\
Choice 4: Both (15y)x and (15x)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 and (15x)y are equivalent representations of (15)xy.