DofotheroU
2021-03-18
Answered

The simplified form of the expression$\sqrt[3]{a}\sqrt[6]{a}\text{}\text{in radicalnotation is}\text{}\sqrt{a}.$

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Fatema Sutton

Answered 2021-03-19
Author has **88** answers

Formula used:

Steps to simplify radical expression:

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.

Positive rational exponents:

$\sqrt[m]{{a}^{n}}={a}^{n\text{/}m}{\textstyle \phantom{\rule{1em}{0ex}}}\text{or}{\textstyle \phantom{\rule{1em}{0ex}}}{a}^{n\text{/}m}=\sqrt[m]{{a}^{n}}$

Power of product:

$\left({x}^{m}\right)}^{n}={x}^{m\cdot n$

Calculation:

Consider the provided expression,$\sqrt[3]{a}\sqrt[6]{a}$

Now, convert the provided radical expression into the exponential notationusing formula of positive rational exponents$\sqrt[m]{{a}^{n}}={a}^{n\text{/}m}$

$\sqrt[3]{a}\sqrt[6]{a}={a}^{1\text{/}3}\cdot {a}^{1\text{/}6}$ ...... (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$\sqrt[3]{a}\sqrt[6]{a}\text{}\text{in radical notation is}\text{}\sqrt{a}.$

Steps to simplify radical expression:

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.

Positive rational exponents:

Power of product:

Calculation:

Consider the provided expression,

Now, convert the provided radical expression into the exponential notationusing formula of positive rational exponents

Now, solve the exponents.

Now put equation (2) in equation (1),

Now convert the exponential expression into radical expression using formula

Therefore, the simplified form of the expression

Jeffrey Jordon

Answered 2021-10-25
Author has **2027** answers

Answer is given below (on video)

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