Question

find the cube root of 4096 by prime factorization method

Answer 1

Step 1: Factor 4,096

4,096 can be written as a product of its prime factors in the following way: 4,096 = 212

The factors were found in the following order: 

4,096 = 2 × 2,048
2,048 = 2 × 1,024
1,024 = 2 × 512
512 = 2 × 256
256 = 2 × 128
128 = 2 × 64
64 = 2 × 32
32 = 2 × 16
16 = 2 × 8
8 = 2 × 4
4 = 2 × 2
2 = 2 × 1

Step 2: Rewrite ∛(4,096)

∛(4,096) =
∛(212) =
∛(212)

∛(212) = ∛(212)

Step 3: Simplify ∛(212)

Step 3.1 Rewrite ∛(212)

∛(212) = ∛(23) × ∛(23) × ∛(23) × ∛(23)

Step 4: Simplify ∛(212)

Step 4.1 Simplify ∛(23)

Using the exponent "product rule", we know that 
∛(23) = ((2)3)⅓ = 2(3×⅓) = 21 = 2

Step 4.2 Simplify ∛(23)

Using the exponent "product rule", we know that 
∛(23) = ((2)3)⅓ = 2(3×⅓) = 21 = 2

Step 4.3 Simplify ∛(23)

Using the exponent "product rule", we know that 
∛(23) = ((2)3)⅓ = 2(3×⅓) = 21 = 2

Step 4.4 Simplify ∛(23)

Using the exponent "product rule", we know that 
∛(23) = ((2)3)⅓ = 2(3×⅓) = 21 = 2

Final Result

∛(4,096) = 2 × 2 × 2 × 2

One real solution was found

16

Answer 2

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