Question

evaluate 8^-1 and 3^-3
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Answer 1

QUESTION :

Evaluate =>

1. ${8}^{ - 1}$
2. ${3}^{ - 3}$

SOLUTION :

1. For evaluation of =>

${8}^{ - 1}$

we must apply the concept -

${a}^{ - 1} = \frac{1}{a}$

Therefore :-

${8}^{ - 1} = \frac{1}{8}$

2. For evaluation of =>

${3}^{ - 3}$

we must apply the concept =>

${a}^{ - r} = \frac{1}{ {a}^{r} }$

therefore :-

${3}^{ - 3} = \frac{1}{ {3}^{3} }$

we know => 3³ = 3×3×3 = 9

so , we get =>

$\frac{1}{ {3}^{3} } = \frac{1}{3} \times \frac{1}{3} \times \frac{1}{3}$

$\frac{1}{9}$

ANSWER :

1.

${8}^{ - 1} = \frac{1}{8}$

2.

${3}^{ - 3} = \frac{1}{9}$

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MORE CONCEPTS RELATED TO EXPONENTS =>

1.

${({a}^{e} )}^{p} = {a}^{e \times p}$

2.

${a}^{e} \times {a}^{h} = {(a)}^{e + h}$

3.

${a}^{e} \div {a}^{f} = {(a)}^{e - f}$

4.

${ (\frac{a}{b}) }^{ - n} = { (\frac{b}{a}) }^{ n}$

5.

${(a)}^{0} = 1$

6.

${ (\frac{a}{b}) }^{m} = \frac{a}{b} \: \times \frac{a}{b} \times \frac{a}{b}..... \: m \: times$