Step:Finding the value using laws of exponents Given ,8^3× 8^ 5× 8^4 Now,we know that 8^3×8^ 5× 8^4=8^3+4 5 nbsp; [∵ a^m× a^n=a^m+n] =8^7 5 =8^2 =64 Hence , ...

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Standard VIII

Mathematics

Constants and Variables

Evaluate:83×8...

Question

Evaluate:
$8^{3} \times 8^{- 5} \times 8^{4}$

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Solution

Step:Finding the value using laws of exponents

Given , $8^{3} \times 8^{- 5} \times 8^{4}$
Now,we know that
$8^{3} \times 8^{- 5} \times 8^{4} = 8^{3 + 4 - 5}$ [ $∵ a^{m} \times a^{n} = a^{m + n}$ ]
$= 8^{7 - 5}$
$= 8^{2}$
$= 64$

Hence ,the value of $8^{3} \times 8^{- 5} \times 8^{4}$ is $64$ .

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Evaluate:

{⎛ ⎜ ⎜ ⎝ \frac{c o s \frac{π}{8} - i s i n \frac{π}{8}}{c o s \frac{π}{8} + i s i n \frac{π}{8}} ⎞ ⎟ ⎟ ⎠}^{4}

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Constants and Variables

Standard VIII Mathematics

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Evaluate: 83×8−5×84

Step:Finding the value using laws of exponents Given ,83×8−5×84 Now,we know that 83×8−5×84=83+4−5 [∵am×an=am+n] =87−5 =82 =64 Hence ,the value of 83×8−5×84 is 64.

Evaluate:
$8^{3} \times 8^{- 5} \times 8^{4}$

Step:Finding the value using laws of exponents

Given , $8^{3} \times 8^{- 5} \times 8^{4}$
Now,we know that
$8^{3} \times 8^{- 5} \times 8^{4} = 8^{3 + 4 - 5}$ [ $∵ a^{m} \times a^{n} = a^{m + n}$ ]
$= 8^{7 - 5}$
$= 8^{2}$
$= 64$

Hence ,the value of $8^{3} \times 8^{- 5} \times 8^{4}$ is $64$ .