Question

solve: 32⅓

•No random letter answer.
•No wrong answer.
•No useless answer.​

Answer 1

Answer:

Step by Step Solution:

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We attempt To simplify the cubed root Of -32

Step 1: Factor -32

-32 can be written as a product of its prime factors in the following way: -32 = -1 × 25

The factors were found in the following order:

-32 = -1 × 32

32 = 2 × 16

16 = 2 × 8

8 = 2 × 4

4 = 2 × 2

2 = 2 × 1

Step 2: Rewrite ∛(-32)

∛(-32) =

∛(-1 x 25) =

∛(-1) × ∛(25)

∛(-1 x 25) = ∛(-1) x ∛(25)

Step 3: Simplify ∛(-1) x ∛(25)

Step 3.1 ∛(-1) will be simplified in the next step

Step 3.2 Rewrite ∛(25)

∛(25) = ∛(-11) × ∛(23) × ∛(22)

Step 4: Simplify ∛(-1) x ∛(25)

Step 4.1 Simplify ∛(-11)

As per raising to the power of one: -1^1 = -1

So, we can rewrite ∛(-11) = ∛(-1) = -1

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 ∛(22)

∛(22) can be rewritten as ∛(4)

∛(4) = 1.5874010519682

Final Result

∛(-32) = -1 × 2 × 1.5874010519682

One real solution was found

-3.1748021039364

Theory And Definitions

Product with same base When multiplying like bases, keep the base the same and add the exponents. In General (xm)×(xn) = x(m+n) and as an example (x2)×(x3) = x(2+3) = x5

The product Of roots rule states that the root of a product Is equal to the root of each factor of the product multiplied together.

Power of one rule states that any number raised to the power of one is the original number itself. In General: x1=x and as an example: 51=5

Answer 2

32⅓

= 32×3 + 1 / 3

= 96+1 / 3

= 97 / 3

= 32.333..........