For problems $$ 4-10 $$, simplify each exponential expression. Write tize expression with only pos exponents. 4. $$ y^{-6} $$ 5. $$ a^{5} \cdot a^{2} $$ 6. $$ x^{0} \cdot y^{-4} $$ 7. $$ \frac{x^{3}}{x^{4}} $$ 8. $$ \left(n^{4}\right)^{5} $$ 9. $$ \frac{a^{5} \cdot b^{2}}{a \cdot b^{6}} $$ 10. $$ x^{4} \cdot\left(x^{-2}\right)^{3} $$ (

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**4. Simplify $$ y^{-6} $$**  
Since a negative exponent indicates the reciprocal, we have:  
$$
y^{-6} = \frac{1}{y^6}
$$

**5. Simplify $$ a^{5} \cdot a^{2} $$**  
When multiplying like bases, we add the exponents:  
$$
a^{5} \cdot a^{2} = a^{5+2} = a^7
$$

**6. Simplify $$ x^{0} \cdot y^{-4} $$**  
Recall that any non-zero number to the power of zero is 1:  
$$
x^{0} = 1
$$  
Thus,  
$$
1 \cdot y^{-4} = y^{-4} = \frac{1}{y^4}
$$

**7. Simplify $$ \frac{x^{3}}{x^{4}} $$**  
When dividing like bases, we subtract the exponents:  
$$
\frac{x^{3}}{x^{4}} = x^{3-4} = x^{-1} = \frac{1}{x}
$$

**8. Simplify $$ \left(n^{4}\right)^{5} $$**  
When raising a power to a power, multiply the exponents:  
$$
\left(n^{4}\right)^{5} = n^{4 \cdot 5} = n^{20}
$$

**9. Simplify $$ \frac{a^{5} \cdot b^{2}}{a \cdot b^{6}} $$**  
Divide the like bases by subtracting their exponents:  
$$
\frac{a^{5}}{a} = a^{5-1} = a^4
$$  
$$
\frac{b^{2}}{b^{6}} = b^{2-6} = b^{-4} = \frac{1}{b^4}
$$  
Thus,  
$$
\frac{a^{5} \cdot b^{2}}{a \cdot b^{6}} = a^4 \cdot \frac{1}{b^4} = \frac{a^4}{b^4}
$$

**10. Simplify $$ x^{4} \cdot \left(x^{-2}\right)^{3} $$**  
First, raise $$ x^{-2} $$ to the third power:  
$$
\left(x^{-2}\right)^{3} = x^{-2 \cdot 3} = x^{-6}
$$  
Then multiply by $$ x^{4} $$:  
$$
x^{4} \cdot x^{-6} = x^{4-6} = x^{-2} = \frac{1}{x^2}
$$
1. $$ y^{-6} = \frac{1}{y^6} $$ 2. $$ a^{5} \cdot a^{2} = a^7 $$ 3. $$ x^{0} \cdot y^{-4} = \frac{1}{y^4} $$ 4. $$ \frac{x^{3}}{x^{4}} = \frac{1}{x} $$ 5. $$ \left(n^{4}\right)^{5} = n^{20} $$ 6. $$ \frac{a^{5} \cdot b^{2}}{a \cdot b^{6}} = \frac{a^4}{b^4} $$ 7. $$ x^{4} \cdot \left(x^{-2}\right)^{3} = \frac{1}{x^2} $$

For problems , simplify each exponential expression. Write tize expression with only pos
exponents.
4.
5.
6.
7.
8.
9.
10.
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For problems , simplify each exponential expression. Write tize expression with only pos exponents. 4. 5. 6. 7. 8. 9. 10. (