Respuesta :

absor201

Answer:

Option B and C  are correct.

Step-by-step explanation:

We need to find the pattern of the values in the table and find the values of a and b.

6³ = 216

216/6 = 36

6² = 36

36/6 = 6

6¹ = 6

6/6 = 1

6⁰ = 1

1/6 = 1/6

6⁻¹ = 1/6

1/6*1/6 = 1/36

6⁻² = 1/36

So, value of a = 1/6

and value of b = 1/36

And we have seen as the exponent is decreasing, each previous value is divided by 6.

So, Option B and C  are correct.

Answer:  The correct options are

(B) the value of b is [tex]\dfrac{1}{36}.[/tex]

(C) As the value of the exponent decreases, each previous value is divided by 6.

Step-by-step explanation:  We are given that Tori examined the pattern of exponents in the following table :

[tex]\textup{power of 6}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\textup{value}\\\\6^3~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~216\\\\6^2~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~36\\\\6^1~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~6\\\\6^0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1\\\\6^{-1}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~a\\\\6^{-2}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~b[/tex]

We are to select the true statements based on the above pattern.

We will be using the following property of exponents :

[tex]x^{-y}=\dfrac{1}{x^y}.[/tex]

Therefore, we get

[tex]a=6^{-1}=\dfrac{1}{6^1}=\dfrac{1}{6}.[/tex]

and

[tex]b=6^{-2}=\dfrac{1}{6^2}=\dfrac{1}{36}.[/tex]

Also, the value of the exponent is decreasing and we see that

[tex]\dfrac{216}{36}=\dfrac{36}{6}=\dfrac{6}{1}=\dfrac{1}{\frac{1}{6}}=\dfrac{\frac{1}{6}}{\frac{1}{36}}=6.[/tex]

So, each previous value is divided by 6.

Thus, the correct options are

(B) the value of b is [tex]\dfrac{1}{36}.[/tex]

(C) As the value of the exponent decreases, each previous value is divided by 6.

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