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

Answer:

The value of x is 20.

Step-by-step 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 $(-2d^5)\times(-2d^5)\times(-2d^5)\times(-2d^5)$

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.

Answer 2

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