Math Problem Statement

Express the number given in exponential form. Fill the exponent in the blank given below. 3√6

Solution

The problem you're asking about involves converting a radical expression into its exponential form.

The expression given is:

63\sqrt[3]{6}

In exponential form, a root can be expressed as a fractional exponent. Specifically, the cube root of a number can be written as that number raised to the power of 13\frac{1}{3}.

So:

63=613\sqrt[3]{6} = 6^{\frac{1}{3}}

This is the expression you're looking for in exponential form.

Would you like more details or have any further questions?

Here are 5 related questions for practice:

  1. How would you express the square root of 9 in exponential form?
  2. How would you write the 4th root of 2 in exponential notation?
  3. Simplify 161416^{\frac{1}{4}}.
  4. What is (613)3(6^{\frac{1}{3}})^3 equal to?
  5. Write 8238^{\frac{2}{3}} as a radical expression.

Tip: Remember, the general rule is xn=x1n\sqrt[n]{x} = x^{\frac{1}{n}}.

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Math Problem Analysis

Mathematical Concepts

Algebra
Exponents
Radicals

Formulas

nth root of a number as x^(1/n)

Theorems

Exponentiation of Radicals

Suitable Grade Level

Grades 6-8