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

Question

UpStudy AI · Accepted Answer

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.

Solución de inteligencia artificial de Upstudy

Responder

Solución

Beyond the Answer

preguntas relacionadas

Latest Pre Algebra Questions