Question

Which of the following is equivalent to 36^(-1/2)?
A)-18
B)-6
C)1/18
D)1/6

Answer 1

Answer:

The correct option is D. The value of given expression is equivalent to $\frac{1}{6}$.

Step-by-step explanation:

The given expression is

$36^{-\frac{1}{2}}$

$36^{-\frac{1}{2}}=\frac{1}{36^{\frac{1}{2}}}$              $[\because a^{-x}=\frac{1}{a^x}]$

$36^{-\frac{1}{2}}=\frac{1}{\sqrt{36}}$                        $[\because a^{\frac{1}{2}}=\sqrt{a}]$

$36^{-\frac{1}{2}}=\frac{1}{6}$

Therefore correct option is D. The value of given expression is equivalent to $\frac{1}{6}$.

Answer 2

Answer:

Option D is correct.

$\frac{1}{6}$ is equivalent to $(36)^{\frac{-1}{2}}$

Step-by-step explanation:

Given : $(36)^{\frac{-1}{2}}$

Find the equivalent expression:

Using rule:

• $(a^n)^m= a^{nm}$
• $a^{-n} =\frac{1}{a^n}$

$(36)^{\frac{-1}{2}}$

⇒$(6^2)^{\frac{-1}{2})$

⇒$(6)^{2 \times \frac{-1}{2}}$

⇒$6^{-1}$ = $\frac{1}{6}$

therefore, the  following equivalent to $(36)^{\frac{-1}{2}}$ is, $\frac{1}{6}$