Answered

Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Get immediate answers to your questions from a wide network of experienced professionals on our Q&A platform. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently.

Which expression is equivalent to [tex]2(5)^4[/tex]?

A. [tex]2 \times 5 \times 4[/tex]

B. [tex]2 \times 5 \times 5 \times 5 \times 5[/tex]

C. [tex]2 \times 4 \times 4 \times 4 \times 4 \times 4[/tex]

D. [tex]10 \times 10 \times 10 \times 10[/tex]

Sagot :

GinnyAnswer
To determine which expression is equivalent to [tex]\(2(5)^4\)[/tex], we need to evaluate each of the given expressions and compare them to the value of [tex]\(2(5)^4\)[/tex].

First, let's calculate [tex]\(2(5)^4\)[/tex]:
- [tex]\(5^4\)[/tex] means multiplying 5 by itself 4 times: [tex]\(5 \times 5 \times 5 \times 5\)[/tex].
- Now, let's calculate [tex]\(5 \times 5 \times 5 \times 5\)[/tex]:
[tex]\[ 5 \times 5 = 25 \][/tex]
[tex]\[ 25 \times 5 = 125 \][/tex]
[tex]\[ 125 \times 5 = 625 \][/tex]
- So, [tex]\(5^4 = 625\)[/tex].
- Now, multiply this result by 2:
[tex]\[ 2 \times 625 = 1250 \][/tex]
Thus, [tex]\(2(5)^4 = 1250\)[/tex].

Next, let's evaluate each of the given expressions and see which one equals 1250:

1. [tex]\(2 \times 5 \times 4\)[/tex]:
[tex]\[ 2 \times 5 = 10 \][/tex]
[tex]\[ 10 \times 4 = 40 \][/tex]
This expression equals 40, which is not equal to 1250.

2. [tex]\(2 \times 5 \times 5 \times 5 \times 5\)[/tex]:
Since we have already computed [tex]\(5^4 = 625\)[/tex], we can just multiply that by 2:
[tex]\[ 2 \times 625 = 1250 \][/tex]
This expression equals 1250, which matches [tex]\(2(5)^4\)[/tex].

3. [tex]\(2 \times 4 \times 4 \times 4 \times 4 \times 4\)[/tex]:
We need to calculate [tex]\(4^5\)[/tex] first:
[tex]\[ 4 \times 4 = 16 \][/tex]
[tex]\[ 16 \times 4 = 64 \][/tex]
[tex]\[ 64 \times 4 = 256 \][/tex]
[tex]\[ 256 \times 4 = 1024 \][/tex]
So, [tex]\(4^5 = 1024\)[/tex].
Now multiply by 2:
[tex]\[ 2 \times 1024 = 2048 \][/tex]
This expression equals 2048, which is not equal to 1250.

4. [tex]\(10 \times 10 \times 10 \times 10\)[/tex]:
[tex]\(10^4\)[/tex] means multiplying 10 by itself 4 times:
[tex]\[ 10 \times 10 = 100 \][/tex]
[tex]\[ 100 \times 10 = 1000 \][/tex]
[tex]\[ 1000 \times 10 = 10000 \][/tex]
This expression equals 10000, which is not equal to 1250.

From these evaluations, we see that the second expression [tex]\(2 \times 5 \times 5 \times 5 \times 5\)[/tex] is equivalent to [tex]\(2(5)^4\)[/tex].

Therefore, the equivalent expression to [tex]\(2(5)^4\)[/tex] is
[tex]\[ 2 \times 5 \times 5 \times 5 \times 5. \][/tex]
Thank you for choosing our service. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We're dedicated to helping you find the answers you need at Westonci.ca. Don't hesitate to return for more.