Question

If 3x-y=123x−y=123, x, minus, y, equals, 12, what is the value of \dfrac{8^x}{2^y} 2 y 8 x ​ start fraction, 8, start superscript, x, end superscript, divided by, 2, start superscript, y, end superscript, end fraction ?

Answer 1

Answer:

Simplify.

Rewrite the expression in the form y^n.

y  ^−13 /  y  ^−7

 

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Step-by-step explanation:

Answer 2

Answer:

$2^{12}=4,096$

Step-by-step explanation:

You know that $3x-y=12$ and have to find

$\dfrac{8^x}{2^y}$

Use the main properties of exponents:

1. $(a^m)^n=a^{m\cdot n}$

2. $\dfrac{a^m}{a^n}=a^{m-n}$

Note that

$8=2^3,$

then

$7^x=(2^3)^x=2^{3\cdot x}=2^{3x}$

Now

$\dfrac{8^x}{2^y}=\dfrac{2^{3x}}{2^y}=2^{3x-y}$

Since $3x-y=12,$ then $2^{3x-y}=2^{12}=4,096$