If 3m- 2n - 18 - 9 - 27 then 3m32n - -

The correct option is B 243 Given, 3^m×2^n = 18 × 9 × 27 #160; = gt; 3^m×2^n = #160; 3 × 3 × 2 × 3 × 3 × 3 × 3 × 3 #160; = gt; 3 ...

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Standard XII

Mathematics

Modulus of a Complex Number

If 3m× 2n =...

Question

If $3^{m} \times 2^{n} = 18 \times 9 \times 27$ then $\frac{3^{m}}{3^{2 n}} =$ ______.

243

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192

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125

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81

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Solution

The correct option is B $243$
Given, $3^{m} \times 2^{n} = 18 \times 9 \times 27$
$=> 3^{m} \times 2^{n} = 3 \times 3 \times 2 \times 3 \times 3 \times 3 \times 3 \times 3$
$=> 3^{m} \times 2^{n} = 3^{7} \times 2^{1}$
$=> m = 7, n = 1$
So, $\frac{3^{m}}{3^{2 n}} = \frac{3^{7}}{3^{2}} = 3^{7 - 2} = 3^{5} = 243$

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Similar questions

3, 9, 27, 81, 243, ?

Q. The value of x if

\sqrt[3]{9 \sqrt[3]{27 \sqrt[3]{81 \sqrt[3]{243}}}} = \sqrt[x]{3^{x + 2}}

, is

Q. Let

A = {1, 3, 5, 7, 9, 11},

B = {3, 9, 27, 81, 243},

then

n [(A \times B) \cap (B \times A)]

Find the value of
$\frac{(18^{3} + 7^{3} + 3 \cdot 18 \cdot 7 \cdot 25)}{3^{6} + 6 \cdot 243 \cdot 2 + 15 \cdot 81 \cdot 4 + 20 \cdot 27 \cdot 8 + 15 \cdot 9 \cdot 16 + 6 \cdot 3 \cdot 32 + 64}$

[(81)^{0.25} \times (9)^{05} \times (27)^{1.5} \div (243)^{0.5}]

is equal to

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If 3m×2n=18×9×27 then 3m32n= ______.

The correct option is B 243Given, 3m×2n=18×9×27 =>3m×2n=3×3×2×3×3×3×3×3=>3m×2n=37×21=>m=7,n=1 So, 3m32n=3732=37−2=35=243

If $3^{m} \times 2^{n} = 18 \times 9 \times 27$ then $\frac{3^{m}}{3^{2 n}} =$ ______.