Question

Simplify 81 power 5/4 A. 3 B. 243 c. 6,561 d. 59,049

Answer 1

Answer:

∛(59,049) - What Is the cubed root of 59,049 ?

This Is the same as (59,049)⅓

Step by Step solution

We attempt To simplify the cubed root Of 59,049

Step 1: Factor 59,049

59,049 can be written as a product of its prime factors in the following way: 59,049 = 310

The factors were found in the following order:

59,049 = 3 × 19,683

19,683 = 3 × 6,561

6,561 = 3 × 2,187

2,187 = 3 × 729

729 = 3 × 243

243 = 3 × 81

81 = 3 × 27

27 = 3 × 9

9 = 3 × 3

Step 2: Rewrite ∛(59,049)

∛(59,049) =

∛(310) =

∛(310)

∛(310) = ∛(310)

Step 3: Simplify ∛(310)

Step 3.1 Rewrite ∛(310)

∛(310) = ∛(33) × ∛(33) × ∛(33) × ∛(31)

Step 4: Simplify ∛(310)

Step 4.1 Simplify ∛(33)

Using the exponent "product rule", we know that

∛(33) = ((3)3)⅓ = 3(3×⅓) = 31 = 3

Step 4.2 Simplify ∛(33)

Using the exponent "product rule", we know that

∛(33) = ((3)3)⅓ = 3(3×⅓) = 31 = 3

Step 4.3 Simplify ∛(33)

Using the exponent "product rule", we know that

∛(33) = ((3)3)⅓ = 3(3×⅓) = 31 = 3

Step 4.4 Simplify ∛(31)

As per raising to the power of one: 3^1 = 3

So, we can rewrite ∛(31) = ∛(3) = 1.44224957030741

Final Result

∛(59,049) = 3 × 3 × 3 × 1.44224957030741

One real solution was found

38.9407383983001

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

Step-by-step explanation:

Answer 2

Answer:

B

Step-by-step explanation: