Answer:
The value of the exponential expression [tex]16^{\frac{1}{4}}[/tex] is 2
Solution:
16 superscript one-fourth= [tex]16^{\frac{1}{4}}[/tex]
As per the problem,
We have to find the value of [tex]16^{\frac{1}{4}}[/tex]
16 in terms of 2 can be written as [tex]2\times2\times2\times2[/tex]
= [tex](2 \times 2 \times 2 \times 2)^{\frac{1}{4}}[/tex]
=[tex]\left(2^{4}\right)^{\frac{1}{4}}[/tex]
As per the exponential rule, [tex]a^{(m)^{n}}=a^{m \times n}[/tex]
=[tex]2^{4 \times \frac{1}{4}}[/tex]
Here, [tex]4\times\frac{1}{4}=1[/tex]
= [tex]2^{1}[/tex]
= 2
Hence, the value is 2.
