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Solve the equation [tex]128 t^7 + 97 = 98[/tex].

Enter all solutions below in integer or reduced fraction form. If there is more than one solution, use a comma to separate the values.

[tex]t =[/tex] __________

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GinnyAnswer
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]
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