Question

Complete the work to simplify the expression (–2d5)4.   1. Express 4 factors of –2d5:     (–2d5)(–2d5)(–2d5)(–2d5) 2. Expand the expression:        –2 ∙ –2 ∙ –2 ∙ –2 ∙ d5∙ d5∙ d5∙ d5 3. Simplify to the exponential form:    (–2)4∙ (d5)4 4. Evaluate the base 2 power:      16 ∙ (d5)4 5. Apply the power of a power:      16dx What is the value of x in the simplified power?

Answer 1

Complete the work to simplify the expression (–2d5)4.

1. Express 4 factors of –2d5:  (–2d5)(–2d5)(–2d5)(–2d5)

2. Expand the expression: –2 ∙ –2 ∙ –2 ∙ –2 ∙ d5∙ d5∙ d5∙ d5

3. Simplify to the exponential form: (–2)4∙ (d5)4

4. Evaluate the base 2 power: 16 ∙ (d5)4

5. Apply the power of a power: 16dx

What is the value of x in the simplified power? x = 20

Answer 2

The value of x is 20.

Explanation:

since on expanding the expression
`(-2d^5)^4` we are given the following steps.

we just need to find the value of 'x'.

step 1: Express 4 factors of
`(-2d^5)^4` as 
`(-2d^5)*(-2d^5)*(-2d^5)*(-2d^5)`

step 2: Expand the expression: –2 ×–2 ×–2 ×–2×d^5×d^5×d^5×d^5

step 3: Simplify to the exponential form: (–2)^4∙ (d^5)^4

step 4: Evaluate the base 2 power: 16 ∙ (d^5)^4 ( as -2×-2×-2×-2=16)

step 5: Apply the power of a power: 16d^20 ( As
`(a^b)^c=(a)^(bc)`

Hence the value of x is: 20.