DofotheroU

## Answered question

2021-03-18

The simplified form of the expression

### Answer & Explanation

Fatema Sutton

Skilled2021-03-19Added 88 answers

Formula used:
Step 1: First convert the radical expression into exponential expressions.
Step 2: Simplify the exponential expression by adding exponents or subtracting exponents.
Step 3: Now, convert the exponential expression into radical expression.
Exponents of positive reason:

Power of product:
${\left({x}^{m}\right)}^{n}={x}^{m\cdot n}$
Calculation:
Consider the provided expression, $\sqrt[3]{a}\sqrt[6]{a}$
Next, use the formula for positive rational exponents to translate the provided radical expression into exponential notation $\sqrt[m]{{a}^{n}}={a}^{n\text{/}m}$
$\sqrt[3]{a}\sqrt[6]{a}={a}^{1\text{/}3}\cdot {a}^{1\text{/}6}$ ...... (1)
Now, solve the exponents.
$\frac{1}{3}+\frac{1}{6}=\frac{2+1}{6}$
$=\frac{3}{6}$ ...... (2)
$=\frac{1}{2}$
Now put equation (2) in equation (1),
${a}^{1\text{/}3}\cdot {a}^{1\text{/}6}={a}^{1\text{/}2}$
Now convert the exponential expression into radical expression using formula
${a}^{n\text{/}m}=\sqrt[m]{{a}^{n}}.$
${a}^{1\text{/}2}=\sqrt{a}$
Therefore, the simplified form of the expression

Jeffrey Jordon

Expert2021-10-25Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?