Question

Can anyone explain how to apply properties of rational exponents ? 3^(1/4) * 27(1/4) ?

Answer 1

Are you looking for the properties of rational exponents or how to solve them?

Answer 2

@Voidus how to solve them

Answer 3

Well, if you know how to solve radical expressions/equations, then you can solve rational exponents.

Here's an example:\[x^{1/n} = \sqrt[n]{x}\]
As you can see, the rational exponent equals n root x, where n is the denomiator.

Another example: \[3^{1/4} = \sqrt[4]{3} \]
that should cover them.

Answer 4

so how would I solve this one? of rational exponents ? 3^(1/4) * 27(1/4)

Answer 5

you first take 3^(1/4) and convert it to the radical expression\[\sqrt[4]{3}\] so you now have \[\sqrt[4]{3}*27(1/4)\] The rest is simple, you just multiply 27 * 1/4:
\[\frac{ 27 }{ 1 }*\frac{ 1 }{ 4 } = \frac{ 27 }{ 4 }\] and convert the numerator to a 4-root radical expression:
\[\frac{ 27 }{ 4} = \frac{ \sqrt[4]{27^4} }{ 4 } = \frac{ \sqrt[4]{531441} }{ 4 } \] and then multiply that by \[\sqrt[4]{3}\] which gets you \[\frac{ \sqrt[4]{531441} * \sqrt[4]{3}}{ 4 } = \frac{ \sqrt[4]{1594323} }{ 4 }\] and you finally get the 4-root and divide that by 4:\[\frac{ \sqrt[4]{1594323} }{ 4 } \approx \frac {35.534}{4} = 8.8835\]