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The value of 362÷92+42 is:
49
36
25
32
32
Use the exponent property (a/b)^n to simplify 36² / 9² as (36/9)2 = 4² = 16. Then add 16 + 4² = 16 + 16 = 32.
Mathematical expression: 36² ÷ 9² + 4²
an÷bn=(a÷b)n
Use the exponent property (a/b)^n to simplify 36² / 9² as (36/9)2 = 4² = 16. Then add 16 + 4² = 16 + 16 = 32.
Students often perform the exponent operations separately: 1296 / 81 = 16, which is correct but time-consuming compared to the division shortcut.
Applying Exponent Rule
Use the property bnan=(ba)n to simplify the division part.
92362=(936)2=42=16
Calculating the Addition
Add the result of the division to the remaining power term 42=16.
16+16=32
D is correct because the expression simplifies to 16 + 16, which equals 32.
Always look for common bases in exponents (like 36 and 9 both being multiples of 9) to simplify fractions before calculating large squares.
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