Final answer:
Sarah's statement that (35^5)^7 equals 3^12 is incorrect because when you raise an exponent to another exponent, you multiply the exponents, resulting in 35^35, not 3^12.
Step-by-step explanation:
Sarah wrote that (35 to the power of 5) to the power of 7 is equal to 3 to the power of 12. To determine the correctness of this statement, we need to apply the rule of exponentiation which states that when an exponent is raised to another exponent, the exponents are multiplied. For the expression Sarah wrote, we would use this rule to find the equivalent single exponent.
Let's apply this to Sarah's equation: (355)7, using the rule, we would multiply the exponents: 5 * 7, which equals 35. This means that (355)7 simplifies to 3535, which is definitely not equal to 312. Therefore, Sarah is incorrect in saying that (355)7 equals 312.