Question

what is the simplified form of 2a with negative 1 over 2

Answer 1

Answer:

• The simplified form of $\left(2a\right)^{-\frac{1}{2}}$  is  $\frac{1}{2^{\frac{1}{2}}a^{\frac{1}{2}}}$.

• In other words:  $\left(2a\right)^{-\frac{1}{2}} =\frac{1}{2^{\frac{1}{2}}a^{\frac{1}{2}}}$

Step-by-step explanation:

From your problem statement, it seems you are asking to simplify the expression 2a with exponent negative 1 over 2.

So,

Considering the expression

$\left(2a\right)^{-\frac{1}{2}}$

Lets simplify step by step

So,

$\left(2a\right)^{-\frac{1}{2}}$

$\mathrm{Apply\:exponent\:rule}:\quad \:a^{-b}=\frac{1}{a^b}$

$\left(2a\right)^{-\frac{1}{2}}=\frac{1}{\left(2a\right)^{\frac{1}{2}}}$

$=\frac{1}{\left(2a\right)^{\frac{1}{2}}}.....[A]$

$\mathrm{Apply\:exponent\:rule}:\quad \left(a\cdot \:b\right)^n=a^nb^n$ on $\left(2a\right)^{\frac{1}{2}}$

$\left(2a\right)^{\frac{1}{2}}=2^{\frac{1}{2}}a^{\frac{1}{2}}$

So putting $\left(2a\right)^{\frac{1}{2}}=2^{\frac{1}{2}}a^{\frac{1}{2}}$ in equation [A]

$=\frac{1}{\left(2a\right)^{\frac{1}{2}}}.....[A]$

$=\frac{1}{2^{\frac{1}{2}}a^{\frac{1}{2}}}$       ∵ $\left(2a\right)^{\frac{1}{2}}=2^{\frac{1}{2}}a^{\frac{1}{2}}$

Therefore, the simplified form of $\left(2a\right)^{-\frac{1}{2}}$  is  $\frac{1}{2^{\frac{1}{2}}a^{\frac{1}{2}}}$

• In other words:  $\left(2a\right)^{-\frac{1}{2}} =\frac{1}{2^{\frac{1}{2}}a^{\frac{1}{2}}}$

Keywords: expression, simplification

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