Find the value of x if 8-95-85- x-A- 316- 98C- 95D- 310

The correct options are C 9^5 D nbsp; nbsp;3^10We know, for non zero integers 'a' and 'b' and any integer 'm', (a/b)^m=(a)^m/(b)^m ⇒(8/9)^5=(8)^5/(9)^5 So, ...

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Byju's Answer

Standard VIII

Mathematics

Exponents with Unlike Bases and Same Exponent

Find the valu...

Question

Find the value of $x$ if $(\frac{8}{9})^{5} = \frac{8^{5}}{x}$ .

3^{16}

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9^{8}

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9^{5}

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3^{10}

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Solution

The correct options are
C $9^{5}$
D $3^{10}$
We know, for non-zero integers 'a' and 'b' and any integer 'm',
$(\frac{a}{b})^{m} = \frac{(a)^{m}}{(b)^{m}}$
$\Rightarrow$ $(\frac{8}{9})^{5} = \frac{(8)^{5}}{(9)^{5}}$
So, the missing value is $9^{5}$ .
But $9^{5} = (3^{2})^{5}$
$= 3^{10}$ $[U s i n g (a^{m})^{n} = a^{m n}]$

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Find the value of x if (89)5=85x.

The correct options are C 95 D 310We know, for non-zero integers 'a' and 'b' and any integer 'm', (ab)m=(a)m(b)m ⇒(89)5=(8)5(9)5 So, the missing value is 95. But 95=(32)5 =310 [Using (am)n=amn]

Find the value of $x$ if $(\frac{8}{9})^{5} = \frac{8^{5}}{x}$ .