Answer:
The value of x is 20.
Step-by-step explanation:
since on expanding the expression [tex](-2d^5)^4[/tex] we are given the following steps.
we just need to find the value of 'x'.
step 1: Express 4 factors of [tex](-2d^5)^4[/tex] as [tex](-2d^5)\times(-2d^5)\times(-2d^5)\times(-2d^5)[/tex]
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 [tex](a^b)^c=(a)^{bc}[/tex]
Hence the value of x is: 20.
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
