Answer :
Which expression have a value of 16/81? check all that apply. (2/3)^4, (16/3)^4, (4/81)^2, and (4/9)^2
Answer:
First and last option is correct.
[tex](\frac{2}{3})^{4}=\frac{16}{81}[/tex]
[tex](\frac{4}{9})^{2}=\frac{16}{81}[/tex]
Step-by-step explanation:
Given:
There are four options.
(2/3)^4, (16/3)^4, (4/81)^2, and (4/9)^2
We need to check all given options for value of 16/81.
Solution:
Using rule.
[tex](\frac{a}{b})^{n}=\frac{a^{n}}{b^{n}}[/tex]
Solve for option [tex](\frac{2}{3})^4[/tex].
[tex](\frac{2}{3})^{4}=\frac{2^4}{3^4}=\frac{2\times 2\times 2\times 2}{3\times 3\times 3\times 3}=\frac{16}{81}[/tex]
Solve for option [tex](\frac{16}{3})^4[/tex].
[tex](\frac{16}{3})^{4}=\frac{16^4}{3^4}=\frac{16\times 16\times 16\times 16}{3\times 3\times 3\times 3}=\frac{65536}{81}[/tex]
Solve for option [tex](\frac{4}{81})^2[/tex].
[tex](\frac{4}{81})^{2}=\frac{4^2}{81^2}=\frac{4\times 4}{81\times 81}=\frac{16}{6561}[/tex]
Solve for option [tex](\frac{4}{9})^2[/tex].
[tex](\frac{4}{9})^{2}=\frac{4^2}{9^2}=\frac{4\times 4}{9\times 9}=\frac{16}{81}[/tex]
Therefore, expression [tex](\frac{2}{3})^4[/tex] and [tex](\frac{4}{9})^2[/tex] have a value of [tex]\frac{16}{81}[/tex].
Answer: Which expressions have a value of StartFraction 16 Over 81 EndFraction? Check all that apply.
Best Option A, D
(A) <===== correct answer
(D) <===== correct answer
Step-by-step explanation: