2. Use the properties of exponents to generate an expression equivalen each of the following expressions. a. $$ 9^{\frac{3}{4}} $$

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To generate an expression equivalent to $$ 9^{\frac{3}{4}} $$ using the properties of exponents, we can follow these steps:

1. **Rewrite the base**: The number 9 can be expressed as a power of 3. Specifically, $$ 9 = 3^2 $$.

2. **Substitute the base into the expression**: We can rewrite $$ 9^{\frac{3}{4}} $$ as:
   $$
   (3^2)^{\frac{3}{4}}
   $$

3. **Apply the power of a power property**: According to the properties of exponents, when raising a power to another power, we multiply the exponents. Therefore:
   $$
   (3^2)^{\frac{3}{4}} = 3^{2 \cdot \frac{3}{4}} = 3^{\frac{6}{4}} = 3^{\frac{3}{2}}
   $$

4. **Simplify the exponent**: The exponent $$ \frac{3}{2} $$ can also be expressed as:
   $$
   3^{\frac{3}{2}} = 3^{1.5} = 3^{1} \cdot 3^{\frac{1}{2}} = 3 \cdot \sqrt{3}
   $$

Thus, the expression $$ 9^{\frac{3}{4}} $$ can be equivalently expressed as:
$$
3^{\frac{3}{2}} \quad \text{or} \quad 3 \cdot \sqrt{3}
$$
$$ 9^{\frac{3}{4}} $$ is equivalent to $$ 3^{\frac{3}{2}} $$ or $$ 3 \cdot \sqrt{3} $$.

Use the properties of exponents to generate an expression equivalen
each of the following expressions.
a.

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