Check the solution to "To simplify: The given expression (2a)(3{a2})"

EunoR

Answered question

2020-10-20

To simplify:
The given expression

(2 \sqrt{a}) (\sqrt{3} {a^{2}})

dessinemoie

Skilled2020-10-21Added 90 answers

Step 1
Law of exponents:
For any rational exponent

\frac{m}{n}

in lowest terms, where m and n are integers and

n > 0,

we define

a^{\frac{m}{n}} = {(\sqrt{n} {a})}^{m} = \sqrt{n} {a^{m}}

If n is even, then we require that

a \geq 0

Step 2
Consider the given expression,

(2 \sqrt{a}) (\sqrt{3} {a^{2}})

By using the law of exponents,

(2 \sqrt{a}) {\sqrt{3} {a^{2}}) = (2 a^{\frac{1}{2}}) (a^{\frac{2}{3}})

= 2 a^{\frac{1}{2}} \cdot a^{\frac{2}{3}}

Applying the exponent rule:

a^{b} \cdot a^{c} = a^{b + c},

we get

= 2 a^{\frac{1}{2} + \frac{2}{3}}

= 2 a^{\frac{7}{6}}

Final Statement:
The simplified form of

(2 \sqrt{a}) (\sqrt{3} {a^{2}})

2 a^{\frac{7}{6}}

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