Final answer:
The equivalent expression for (5² • 3⁴)³ is 5⁶ • 3¹², applying the rule of exponentiation by raising each factor to the exponent separately and thereby multiplying the original exponents by 3.
Step-by-step explanation:
Equivalent Expression for Exponentials when Cubed
The goal here is to find an equivalent expression for the given exponential expression (5² • 3⁴)³. To simplify, we can use the rule of exponentiation where when we raise a product to an exponent, we raise each factor within the product to that exponent separately. Therefore, (5²)³ becomes 5⁽²ˣ³⁾, which equals 5⁶. Similarly, (3⁴)³ becomes 3⁽⁴ˣ³⁾, which equals 3¹². Multiplying these together gives us our final equivalent expression: 5⁶ • 3¹².
As an example to illustrate this concept, consider (5³)⁴. This would expand to (5• 5 • 5) multiplied by itself four times, which is equivalent to fifteen fives multiplied together, or 5¹². Simply put, we have multiplied the exponents 3 and 4 together to arrive at the final exponent, 12.
Similarly, for the given problem, the operation performed on the bases and exponents results in the multiplication of the individual exponents by 3.