Question

(-2)-². is equal to. ??​

Answer 1

Given :   (-2)⁻²

To Find : Evaluate

Solution:

Law of exponents

${{\text{a}}^{n}}\times {{a}^{-n}}=1\text{ or }{{\text{a}}^{n}}=\frac{1}{{{a}^{n}}} \\ & {{a}^{m}}\times {{a}^{n}}={{a}^{m+n}} \\ & \frac{{{a}^{m}}}{{{a}^{n}}}={{a}^{m-n}} \\ & {{\left( {{a}^{m}} \right)}^{n}}={{\left( {{a}^{n}} \right)}^{m}}={{a}^{mn}} \\ & {{a}^{m}}\times {{b}^{m}}={{\left( ab \right)}^{m}} \\ & \frac{{{a}^{n}}}{{{b}^{n}}}={{\left( \frac{a}{b} \right)}^{n}} \\ & {{a}^{0}}=1$

(-2)⁻²

= 1/(-2)²

= 1/(-1 * 2)²

= 1/{(-1)² * 2²}

(-1)ⁿ = 1 when n is even and = - 1 when n is odd

(-1)² = 1

2² = 4

= 1/(1 * 4)

= 1/4

Hence (-2)⁻²  = 1/4

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