4. $$ -\sqrt[3]{-70 a^{18} b^{6}+6 a^{18} b^{6}} $$ 5. $$ \sqrt[3]{27 x^{12}}-\sqrt{25 x^{8}} $$ 6. $$ -\sqrt{100 x^{70} y^{26}} $$ 7. $$ \sqrt{81 x^{14} y^{2}} $$ 8. $$ -\sqrt[3]{-512 a^{27} b^{15}} $$ 9. $$ \sqrt{p^{100} q^{16}} $$

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4. Factor out $$a^{18} b^{6}$$:
$$
-\sqrt[3]{-70a^{18} b^{6}+6a^{18} b^{6} } = -\sqrt[3]{(-70+6)a^{18}b^{6}} = -\sqrt[3]{-64a^{18}b^{6}}.
$$
Taking the cube root:
$$
\sqrt[3]{-64} = -4,\quad \sqrt[3]{a^{18}} = a^6,\quad \sqrt[3]{b^{6}} = b^2.
$$
Thus,
$$
-\sqrt[3]{-64a^{18}b^{6}} = -(-4a^6b^2) = 4a^6b^2.
$$

5. Simplify each radical separately:
$$
\sqrt[3]{27x^{12}} = \sqrt[3]{27}\cdot \sqrt[3]{x^{12}} = 3x^4,
$$
since $$27 = 3^3$$ and $$x^{12} = \left(x^4\right)^3$$. Also,
$$
\sqrt{25x^{8}} = \sqrt{25}\cdot \sqrt{x^{8}} = 5x^4,
$$
because $$25 = 5^2$$ and $$x^{8} = \left(x^4\right)^2$$. Therefore,
$$
\sqrt[3]{27x^{12}}-\sqrt{25x^{8}} = 3x^4-5x^4 = -2x^4.
$$

6. Break up the square root:
$$
-\sqrt{100x^{70}y^{26}} = -\sqrt{100}\cdot\sqrt{x^{70}}\cdot\sqrt{y^{26}}.
$$
Since 
$$
\sqrt{100} = 10,\quad x^{70}=(x^{35})^2,\quad y^{26}=(y^{13})^2,
$$
we have
$$
\sqrt{x^{70}} = x^{35} \quad\text{and}\quad \sqrt{y^{26}} = y^{13}.
$$
Thus,
$$
-\sqrt{100x^{70}y^{26}} = -10x^{35}y^{13}.
$$

7. Factor the radicand:
$$
\sqrt{81x^{14}y^{2}} = \sqrt{81}\cdot\sqrt{x^{14}}\cdot\sqrt{y^{2}}.
$$
Note that:
$$
\sqrt{81} = 9,\quad x^{14}=(x^{7})^2,\quad y^{2}=(y)^2.
$$
So,
$$
\sqrt{x^{14}} = x^7,\quad \sqrt{y^{2}} = y.
$$
Therefore,
$$
\sqrt{81x^{14}y^{2}} = 9x^7y.
$$

8. Evaluate the cube root:
$$
-\sqrt[3]{-512a^{27}b^{15}}.
$$
Since:
$$
\sqrt[3]{-512} = -8,\quad \sqrt[3]{a^{27}} = a^9,\quad \sqrt[3]{b^{15}} = b^5,
$$
the cube root becomes:
$$
\sqrt[3]{-512a^{27}b^{15}} = -8a^9b^5.
$$
Including the negative sign outside,
$$
-\sqrt[3]{-512a^{27}b^{15}} = -(-8a^9b^5) = 8a^9b^5.
$$

9. Simplify the square root:
$$
\sqrt{p^{100}q^{16}} = \sqrt{p^{100}}\cdot\sqrt{q^{16}}.
$$
Since:
$$
\sqrt{p^{100}} = p^{50}\quad\text{and}\quad \sqrt{q^{16}} = q^8,
$$
we obtain:
$$
\sqrt{p^{100}q^{16}} = p^{50}q^8.
$$
4. $$ 4a^6b^2 $$ 5. $$ -2x^4 $$ 6. $$ -10x^{35}y^{13} $$ 7. $$ 9x^7y $$ 8. $$ 8a^9b^5 $$ 9. $$ p^{50}q^8 $$

4. \( -\sqrt[3]{-70 a^{18} b^{6}+6 a^{18} b^{6}} \) 5. \( \sqrt[3]{27 x^{12}}-\sqrt{25 x^{8}} \) 6. \( -\sqrt{100 x^{70} y^{26}} \) 7. \( \sqrt{81 x^{14} y^{2}} \) 8. \( -\sqrt[3]{-512 a^{27} b^{15}} \) 9. \( \sqrt{p^{100} q^{16}} \)

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