Test In Rational Exponents

Which of these is correct:

Which of these is correct:

Is the following statement true or false? \( a^{\frac{m}{n}}=\sqrt[n]{a^m}\)

Evaluate the expression \(8^{\frac13}\)

Evaluate the expression \(4^{\frac32}\)

Evaluate the expression \(32^{\frac45}\)

Evaluate the expression \((-8)^{\frac23}\)

Is the following statement true or false? \( 0^{-\frac12} = 0\)

Is the following statement true or false? \( (-1)^{-\frac{1}{2}} = 1\)

Is the following statement true or false? \((-4)^{\frac32} = -8\)

Is the following statement true or false? \( -4^{\frac32} = -8\)

Simplify the expression \(a^{\frac12}\cdot a^{\frac32}\)

Simplify the expression \(\frac{x^2 \cdot x^{\frac32}}{x^{\frac12}}\)

Simplify the expression \(\frac{a^3 \cdot a^{\frac14}}{a^{\frac54} \cdot a^{-\frac32}}\)