Question

Please do it quickly, because Tomorrow is my exam

Simplify (27/8)^5×(27/8)^p=(3/2)^18

Answer 1

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Answer 2

Hi there!
Here's the answer:

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¶¶¶ Identities Used :

• $a^{m} × a^{n} = a^{mn}$

• $\frac{a^{m}}{b^{m}} = (\frac{a}{b})^{m}$

• $a^{m}^{n} = a^{mn}$

• $If\: a^{m} = a^{n}\: then\: m = n$

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SOLUTION:

$(\frac{27}{8})^{5} × (\frac{27}{8})^{p} = (\frac{3}{2})^{18}$

=> $(\frac{27}{8})^{5+p} = (\frac{3}{2})^{18}$

$27 = 3^{3}$
$8 = 2^{3}$

=> $(\frac{3^{3}}{2^{3}})^{5+p} = (\frac{3}{2})^{18}$

=> $[(\frac{3}{2})^{3}]^{5+p} = (\frac{3}{2})^{18}$

=> $(\frac{3}{2})^{3(5+p)} = (\frac{3}{2})^{18}$

=> $(\frac{3}{2})^{15 + 3p} = (\frac{3}{2})^{18}$

Bases are Equal, So Powers are also equal
=> 15 + 3p = 18
=> 3p = 18 - 15
=> 3p = 3
=> p = 1

•°• p = 1

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