Question
Given that the fourth root of 16 is 2, what is 16 5/4
?(1 point)
?(1 point)
Answers
GPT-4o mini
To find \( 16^{5/4} \), we can break it down using the property of exponents:
\[
16^{5/4} = (16^{1/4})^5
\]
Since we know that \( 16^{1/4} = 2 \), we can substitute that into the equation:
\[
(16^{1/4})^5 = 2^5
\]
Now we calculate \( 2^5 \):
\[
2^5 = 32
\]
Therefore, \( 16^{5/4} = 32 \).
\[
16^{5/4} = (16^{1/4})^5
\]
Since we know that \( 16^{1/4} = 2 \), we can substitute that into the equation:
\[
(16^{1/4})^5 = 2^5
\]
Now we calculate \( 2^5 \):
\[
2^5 = 32
\]
Therefore, \( 16^{5/4} = 32 \).