Question
The value of $\left[2^{-1} \times 3^{-1}\right]^{-1}$ is _________.
✓
Answer
The value of $\left[2^{-1} \times 3^{-1}\right]^{-1}$ is 6.
Solution:
Using law of exponents, $\text{a}^{-\text{m}}=\frac{1}{\text{a}^{\text{m}}}$ [$\because$ a is non-zero integer]
$\therefore$ $\big[2^{-1}\times3^{-1}\big]^{-1}=\Big(\frac{1}{2}\times\frac{1}{3}\Big)^{-1}$
$=\Big(\frac{1}{6}\Big)^{-1}=6$
Hence,
$\big[2^{-1}\times3^{-1}\big]^{-1}=6$
Solution:
Using law of exponents, $\text{a}^{-\text{m}}=\frac{1}{\text{a}^{\text{m}}}$ [$\because$ a is non-zero integer]
$\therefore$ $\big[2^{-1}\times3^{-1}\big]^{-1}=\Big(\frac{1}{2}\times\frac{1}{3}\Big)^{-1}$
$=\Big(\frac{1}{6}\Big)^{-1}=6$
Hence,
$\big[2^{-1}\times3^{-1}\big]^{-1}=6$
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