Final answer:
The equivalent expression to 9 to the power of 2 multiplied by 9 to the power of 6 is 9 to the power of 8 over 9 to the power of 7, which simplifies to 9 to the power of 2.
Step-by-step explanation:
The question is asking for an equivalent expression to 9 to the power of 2 multiplied by 9 to the power of 6. When multiplying numbers with the same base, you add the exponents, according to the rules of exponents. Thus, 9² ⋅ 9¶ is equivalent to 9 to the power of 8. Another option that could potentially be equivalent would involve division of two powers of nine, which must result in 9 to the power of 2 (9¸/9·), because when dividing powers with the same base, you subtract the exponents.
The other provided options do not correctly apply the rules of exponents and therefore are not equivalent to 9² ⋅ 9¶. The correct answer to what is equivalent to 9² ⋅ 9¶ is 9 to the power of 8 over 9 to the power of 7. This simplifies to just 9 to the power of 2 because 8 minus 7 equals 1.