76) √x-1:
 77)  √3x-4:
78) ∜x:
79) ³√x-1:
  80) √x:

Let's break down each of the expressions individually:

**76) \( \sqrt{x - 1} \):**
This represents the square root of the expression \( x - 1 \), which means:

\[
\sqrt{x - 1} = (x - 1)^{1/2}
\]

**77) \( \sqrt{3x - 4} \):**
This represents the square root of the expression \( 3x - 4 \), which means:

\[
\sqrt{3x - 4} = (3x - 4)^{1/2}
\]

**78) \( \sqrt[4]{x} \):**
This represents the fourth root of \( x \), which means:

\[
\sqrt[4]{x} = x^{1/4}
\]

**79) \( \sqrt[3]{x - 1} \):**
This represents the cube root of the expression \( x - 1 \), which means:

\[
\sqrt[3]{x - 1} = (x - 1)^{1/3}
\]

**80) \( \sqrt{x} \):**
This represents the square root of \( x \), which is the same as \( x \) raised to the power of \( 1/2 \):

\[
\sqrt{x} = x^{1/2}
\]

Each of these expressions involves fractional exponents, indicating roots of various degrees.

Would you like further details or have any questions?

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Here are 5 related questions to expand your understanding:

1. How do you differentiate \( \sqrt{x - 1} \) with respect to \( x \)?
2. What is the domain of the function \( \sqrt{3x - 4} \)?
3. How do you solve the equation \( \sqrt[4]{x} = 2 \)?
4. What is the simplified form of \( (\sqrt[3]{x - 1})^3 \)?
5. How does \( \sqrt{x} \) behave as \( x \to 0 \)?

**Tip:** When solving equations with roots, always check if extraneous solutions are introduced by squaring both sides!

76) √x-1: 77) √3x-4: 78) ∜x: 79) ³√x-1: 80) √x:

Explore the mathematical concepts behind roots and fractional exponents with expressions like √x-1, √3x-4, ∜x, ³√x-1, and √x. Learn about the properties of exponents and how to simplify radical expressions, suitable for students in Grades 9-12.

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