To solve the equation [tex]\(128 t^7 + 97 = 98\)[/tex], let's go through the steps systematically.
1. Start by isolating the term containing [tex]\(t\)[/tex]:
[tex]\[
128 t^7 + 97 = 98
\][/tex]
2. Subtract 97 from both sides:
[tex]\[
128 t^7 = 98 - 97
\][/tex]
[tex]\[
128 t^7 = 1
\][/tex]
3. Now, we need to solve for [tex]\(t\)[/tex]:
[tex]\[
t^7 = \frac{1}{128}
\][/tex]
4. To find [tex]\(t\)[/tex], we take the 7th root of both sides:
[tex]\[
t = \left(\frac{1}{128}\right)^{\frac{1}{7}}
\][/tex]
5. Evaluate the expression:
[tex]\[
t = 0.5
\][/tex]
Thus, the solution to the equation [tex]\(128 t^7 + 97 = 98\)[/tex] is:
[tex]\[
t = \boxed{0.5}
\][/tex]
