Sarah wrote that \((3^5)^7 = 3^{12}\). Correct her mistake. Write an exponential expression using a base of 3 and exponents of 5, 7, and 12 that would make her answer correct.
Explanation: Sarah's mistake is in calculating \((3^5)^7\). The correct calculation is \((3^5)^7 = 3^{35}\) because when raising a power to another power, you multiply the exponents: \(5 \times 7 = 35\).
To make her answer correct using the exponents 5, 7, and 12, the expression could be: \(3^{5+7} = 3^{12}\).
Answer (3)
( 3 5 ) 7 = 3 5 ⋅ 7 = 3 35 = 3 12 3 5 ⋅ 3 7 = 3 5 + 7 = 3 12
( 3 5 ) 7 = 3 5 ⋅ 7 = 3 35 3 5 ⋅ 3 7 = 3 5 + 7 = 3 12
Sarah's calculation of ( 3 5 ) 7 was incorrect because she added the exponents instead of multiplying them. The correct evaluation is ( 3 5 ) 7 = 3 35 . To relate her answer correctly with the exponent 12, 3 5 ⋅ 3 7 = 3 12 is an appropriate expression.
;
