Question

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If 3x−y=12, what is the value of
$\sf{ \frac{ {8}^{x} }{ {2}^{y} }}\ \textless \ br /\ \textgreater \ ?\ \textless \ br /\ \textgreater$


A) 212

B) 44

C) 82

D) The value cannot be determined from the information given.

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Answer 1

Answer:

$3x - y = 12 \\ \\ = > 3x = 12 + y \\ \\ \frac{8 {}^{x} }{2 {}^{y} } \\ \\ = \frac{(2 {}^{3}) {}^{x} }{2 {}^{y} } \\ \\ = \frac{2 {}^{3x} }{2 {}^{y} } \\ \\ = 2 {}^{3x - y} \\ \\ \: \: \: \: \: = {2}^{12 + y - y} \: \: \: \: (3x = 12 + y) \\ \\ = {2}^{12} \\ \\ = 4096 \\ \\ formula \: \: \: \: - \: \: \: (x {}^{m} ) {}^{n} = x {}^{m.n} \\ \\ \frac{x {}^{m} }{x {}^{n} } = x {}^{m - n}$

Answer 2

Required Answer:-

Given:

• 3x - y = 12

To Find:

• The value of 8ˣ/2ʸ

Solution:

We have,

➡ 3x - y = 12

So,

8ˣ/2ʸ

= 2³ˣ/2ʸ

We know that,

➡ aˣ/aʸ = aˣ⁻ʸ

Using this formula, we get,

= 2³ˣ⁻ʸ

Now,

➡ 3x - y = 12

➡ 2³ˣ⁻ʸ = 2¹²

➡ 2³ˣ⁻ʸ = 4096

★ Hence, the value of 2³ˣ⁻ʸ is 4096.

Answer:

• 2³ˣ⁻ʸ = 4096

More Formulae:

• a⁰ = (a ≠ 0)
• aˣ = 1/a⁻ˣ
• √a = a
• (aˣ)ʸ = aˣʸ
• aˣ × aʸ = aˣ ⁺ ʸ