Find the value of -n- if 9-2-9n-91A- 9B- 6C- 7D- 5

The correct option is C 7By the Laws of Exponents, we know that a^m/a^n=a^m n Given (9)^18/(9)^n=9^11 ⇒9^18 n=9^11, since the bases are same so equating the ex ...

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Standard VII

Mathematics

Division of Exponents Having the Same Base

Find the valu...

Question

Find the value of 'n' if $\frac{(9)^{18}}{(9)^{n}} = 9^{11}$

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Solution

The correct option is C 7
By the Laws of Exponents, we know that $\frac{a^{m}}{a^{n}} = a^{m - n}$
Given $\frac{(9)^{18}}{(9)^{n}} = 9^{11}$
$\Rightarrow$ $9^{18 - n} = 9^{11}$ , since the bases are same so equating the exponents
$18 - n = 11 \Rightarrow n = 18 - 11 = 7$

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Find the value of 'n' if (9)18(9)n=911

The correct option is C 7By the Laws of Exponents, we know that aman=am−n Given (9)18(9)n=911 ⇒918−n=911, since the bases are same so equating the exponents 18−n=11⇒n=18−11=7

Find the value of 'n' if $\frac{(9)^{18}}{(9)^{n}} = 9^{11}$

The correct option is C 7
By the Laws of Exponents, we know that $\frac{a^{m}}{a^{n}} = a^{m - n}$
Given $\frac{(9)^{18}}{(9)^{n}} = 9^{11}$
$\Rightarrow$ $9^{18 - n} = 9^{11}$ , since the bases are same so equating the exponents
$18 - n = 11 \Rightarrow n = 18 - 11 = 7$