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Chapter 0: Problem 92

Convert the expressions to radical form. $$ \frac{4}{5} x^{3 / 2} $$

Short Answer

Expert verified
The given expression is converted to radical form as follows: \(\frac{4}{5}x^{3/2} = \frac{4}{5}\sqrt{x^3}\). This expression is in its simplest radical form.

Step by step solution

01

Rewrite the fractional exponent as a radical

The given expression is \[ \frac{4}{5}x^{3/2}. \] The exponent part \(3/2\) consists of two parts, where the numerator 3 corresponds to the power of x, and the denominator 2 corresponds to the root of x. We rewrite this expression using the relevant root symbol: \[ \frac{4}{5}\sqrt{x^3}. \]
02

Simplify the radical expression

Now we have successfully transformed the expression to radical form, but we can still simplify it further if possible. In this case, there are no additional simplifications needed, so the final answer is: \[ \frac{4}{5}\sqrt{x^3}. \]

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Most popular questions from this chapter

Convert each expression in Exercises into its technology formula equivalent as in the table in the text.\(\frac{2}{3+5^{7-9}}\)

Solve the equation for \(x\) (mentally, if possible). \(3 x+1=x\)

By any method, determine all possible real solutions of each equation Check your answers by substitution. \(-x^{2}-2 x-1=0\)

\(\left(x^{3}+1\right) \sqrt{x+1}-\left(x^{3}+1\right)^{2} \sqrt{x+1}\)

Find all possible real solutions of each equation \(2 x^{6}-x^{4}-2 x^{2}+1=0\)
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