Final answer:
The equivalent expression to 21³∘15 - 9³ ∘15 is found by factoring out the common term and then simplifying, which results in 12³∘15. option D is the correct answer.
Step-by-step explanation:
The student is asking for the expression that is equivalent to 21³∙15 - 9³ ∙15. To find the equivalent expression, we can factor out the common term ³∙15 from both parts of the expression, which gives us:
(21 - 9)³∙15
Simplifying the expression inside the parentheses gives us 12³∙15, which is the equivalent expression. Option D, 12³∘15, is the correct answer.
To simplify the expression 21³√15 - 9³ √15, we can combine the terms with the same radical. This gives us 12√15 as the equivalent expression.
To simplify the expression 21³√15 - 9³ √15, we can find the cube root of 15 which is √15. Therefore, the expression becomes 21√15 - 9√15. Since the terms have the same radical, we can combine them. This gives us (21 - 9)√15 which simplifies to 12√15. Therefore, the expression 21³√15 - 9³ √15 is equivalent to 12√15.