Simplify the following- 81-1-4

Given: (81)^ 1/4,Now we use a^ n=1/a^nHere a=81 and n=1/4(81)^ 1/4=1/(81)^1/4 =1/(3× 3× 3× 3)^1/40ex0ex=1/(3^4)^1/40ex0ex=1/3Hence, (81)^ 1/4=1/3. ...

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Standard VIII

Mathematics

Powers with Negative Exponents

Simplify the ...

Question

Simplify the following: $(81)^{- \frac{1}{4}}$

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Solution

Given: $(81)^{- \frac{1}{4}}$ ,
Now we use $a^{- n} = \frac{1}{a^{n}}$
Here $a = 81$ and $n = \frac{1}{4}$
$(81)^{- \frac{1}{4}} = \frac{1}{(81)^{\frac{1}{4}}}$
$= \frac{1}{(3 \times 3 \times 3 \times 3)^{\frac{1}{4}}} = \frac{1}{{(3^{4})}^{\frac{1}{4}}} = \frac{1}{3}$
Hence, $(81)^{- \frac{1}{4}} = \frac{1}{3}$ .

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Simplify the following: (81)-14

Given: (81)-14,Now we use a-n=1anHere a=81 and n=14(81)-14=1(81)14 =1(3×3×3×3)14=13414=13Hence, (81)-14=13.

Simplify the following: $(81)^{- \frac{1}{4}}$