Question

Rewrite the expression

What is the radical expression that is equivalent to the expression (35)^1/4?
Enter your answer as a radical.

Answer 1

The radical expression equivalent to (35)^1/4 is the fourth root of 35, written as √^4 35 or 35^1/4.

Step-by-step explanation:

The radical expression that is equivalent to the expression (35)^1/4 is the fourth root of 35, which can be denoted as √435 or 351/4. In general, when we raise a number to a fractional power, the numerator of the fraction indicates the power and the denominator indicates the root. Hence, raising 35 to the 1/4 power is equivalent to taking the fourth root of 35. This operation involves finding a number which, when multiplied by itself four times, equals 35. While this cannot be simplified to an integer or simple fraction, it can be estimated using a calculator or left in radical form for exact representation.

Answer 2

`\sqrt[n]{a^m}=a^(m)/(n)`

`35^(1)/(4)=\sqrt[4]{35}`

`(3^5)^(1)/(4)=3^{5\cdot(1)/(4)}=3^(5)/(4)=3^{1(1)/(4)}=3\cdot3^(1)/(4)=3\sqrt[4]3`

`Used:\\(a^n)^m=a^(n\cdot m)\\\\a^n\cdot a^m=a^(n+m)`