Simplify the expression (30x⁴)/(3x⁻²).

We can separate the coefficients and the variables.

$$\frac{30x^4}{3x^{-2}} = \left(\frac{30}{3}\right) \times \left(\frac{x^4}{x^{-2}}\right)$$

First, simplify the coefficients:

$$\frac{30}{3} = 10$$

Next, simplify the terms with $x$ using the rule $\frac{a^m}{a^n} = a^{m-n}$:

$$\frac{x^4}{x^{-2}} = x^{4 - (-2)} = x^{4+2} = x^6$$

Combine the simplified parts:

$$10 \times x^6 = 10x^6$$ $$\boxed{10x^6}$$

Use the rule $\left(\frac{a}{b}\right)^{-n} = \left(\frac{b}{a}\right)^n$:

$$\left(\frac{x^5}{2t^3}\right)^{-4} = \left(\frac{2t^3}{x^5}\right)^4$$

Now, apply the power of 4 to each term in the numerator and the denominator using the rule $(ab)^n = a^n b^n$ and $(a^m)^n = a^{mn}$:

$$\left(\frac{2t^3}{x^5}\right)^4 = \frac{(2)^4 (t^3)^4}{(x^5)^4}$$

Calculate the powers:

$$(2)^4 = 2 \times 2 \times 2 \times 2 = 16$$ $$(t^3)^4 = t^{3 \times 4} = t^{12}$$ $$(x^5)^4 = x^{5 \times 4} = x^{20}$$

Substitute these back into the expression:

$$\frac{16t^{12}}{x^{20}}$$ $$\boxed{\frac{16t^{12}}{x^{20}}}$$

$\frac{x^5 y^4 z^{-4}}{x^{-2} y^2 z^{-1}}$.
Apply the rule $\frac{a^m}{a^n} = a^{m-n}$ to each variable separately:
For $x$:

$$\frac{x^5}{x^{-2}} = x^{5 - (-2)} = x^{5+2} = x^7$$

For $y$:

$$\frac{y^4}{y^2} = y^{4-2} = y^2$$

For $z$:

$$\frac{z^{-4}}{z^{-1}} = z^{-4 - (-1)} = z^{-4+1} = z^{-3}$$

Combine the simplified terms. Use the rule $a^{-n} = \frac{1}{a^n}$ for $z^{-3}$:

$$x^7 y^2 z^{-3} = \frac{x^7 y^2}{z^3}$$ $$\boxed{\frac{x^7 y^2}{z^3}}$$