The value of the expression is [tex]0.25[/tex]
Explanation:
The expression is [tex]$\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)^{-2}$[/tex]
Since, the base of the expression is the same. Then, by "product rule", when multiplying two powers that have the same base, you can add the exponents.
Thus, we have,
[tex]$\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)^{-2}=\left(\frac{1}{2}\right)^{4-2}$[/tex]
Adding the exponents, we have,
[tex]$\left(\frac{1}{2}\right)^{4}\left(\frac{1}{2}\right)^{-2}=\left(\frac{1}{2}\right)^{2}$[/tex]
Applying exponent rule, [tex]$\left(\frac{a}{b}\right)^{c}=\frac{a^{c}}{b^{c}}$[/tex], we have,
[tex]$\left(\frac{1}{2}\right)^{2}=\frac{1^{2}}{2^{2}}$[/tex]
Simplifying, we get,
[tex]\frac{1}{4}[/tex]
Dividing, we have,
[tex]0.25[/tex]
Thus, the value of the expression is [tex]0.25[/tex]
