Question

A student simplified (cube root of 27 − 14 ÷ 2)(6 − 8)2 using the following steps: (cube root of 27 − 14 ÷ 2)(6 − 8)2 Step 1: (3 − 14 ÷ 2)(6 − 8)2 Simplify the cube root. Step 2: (−11 ÷ 2) (6 − 8)2 Subtract within first parentheses. Step 3: −5.5(6 − 8)2 Divide within the first parentheses. Step 4: −5.5(6 − 64) Simplify the exponent. Step 5: −5.5(−58) Subtract within the parentheses. Step 6: 319 Multiply.
Part A: The student made a mistake in Step 2. Describe the mistake and explain how to correct it. (3 points)

Part B: The student made a mistake in Step 4. Describe the mistake and explain how to correct it. (3 points)

Part C: Show every step of your work to simplify (cube root of 27 − 14 ÷ 2)(6 − 8)2. (6 points)

Answer 1

Answer:

Step-by-step explanation:

Calculator Use

Use this calculator to find the cube root of positive or negative numbers. Given a number x, the cube root of x is a number a such that a3 = x. If x positive a will be positive, if x is negative a will be negative. Cube roots is a specialized form of our common radicals calculator.

Example Cube Roots:

The 3rd root of 64, or 64 radical 3, or the cube root of 64 is written as 64−−√3=4.

The 3rd root of -64, or -64 radical 3, or the cube root of -64 is written as −64−−−−√3=−4.

The cube root of 8 is written as 8–√3=2.

The cube root of 10 is written as 10−−√3=2.154435.

The cube root of x is the same as x raised to the 1/3 power. Written as x−−√3=x13. The common definition of the cube root of a negative number is that

(-x)1/3 = -(x1/3).[1] For example:

The cube root of -27 is written as −27−−−−√3=−3.

The cube root of -8 is written as −8−−−√3=−2.

The cube root of -64 is written as −64−−−−√3=−4.

Cube roots (for integer results 1 through 10)

Cube root of 1 is 1

Cube root of 8 is 2

Cube root of 27 is 3

Cube root of 64 is 4

Cube root of 125 is 5

Cube root of 216 is 6

Cube root of 343 is 7

Cube root of 512 is 8

Cube root of 729 is 9

Cube root of 1000 is 10

To calculate fractional exponents use our calculator for Fractional Exponents.