IDNLearn.com: Your trusted source for finding accurate and reliable answers. Our experts provide timely and precise responses to help you understand and solve any issue you face.

What is the value of the expression below?

[tex]\[ \left(625^2\right)^{1 / 8} \][/tex]

A. 25
B. 125
C. 5
D. 1


Sagot :

Let's solve the expression [tex]\(\left(625^2\right)^{1 / 8}\)[/tex] step-by-step.

1. First, consider the inner part of the expression: [tex]\(625^2\)[/tex].
2. We know that [tex]\(625 = 25^2\)[/tex]. Therefore, [tex]\(625^2\)[/tex] can be rewritten as:
[tex]\[ (25^2)^2 \][/tex]
3. According to the laws of exponents, [tex]\((a^m)^n = a^{mn}\)[/tex], so:
[tex]\[ (25^2)^2 = 25^{2 \cdot 2} = 25^4 \][/tex]
4. Now we need to evaluate [tex]\((25^4)^{1/8}\)[/tex].
5. Again, using the laws of exponents [tex]\((a^m)^{1/n} = a^{m/n}\)[/tex], we can rewrite the expression as:
[tex]\[ 25^{4 \cdot \frac{1}{8}} = 25^{\frac{4}{8}} = 25^{\frac{1}{2}} \][/tex]
6. The expression [tex]\(25^{\frac{1}{2}}\)[/tex] represents the square root of 25:
[tex]\[ 25^{\frac{1}{2}} = \sqrt{25} \][/tex]
7. We know that [tex]\(\sqrt{25} = 5\)[/tex].

Hence, the value of the expression [tex]\(\left(625^2\right)^{1 / 8}\)[/tex] is [tex]\(5\)[/tex].

Therefore, the correct answer is:
C. 5
Thank you for participating in our discussion. We value every contribution. Keep sharing knowledge and helping others find the answers they need. Let's create a dynamic and informative learning environment together. For trustworthy answers, visit IDNLearn.com. Thank you for your visit, and see you next time for more reliable solutions.