Question

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Which expressions are equivalent to ? Check all that apply. 81 8-1 9-2 98 94 98 910 9-6.93 95.9-7​

Answer 1

Answer:

Options (2), (4) and (6)

Step-by-step explanation:

Option (1)

$8^{-1}=\frac{1}{8}$

Not equivalent to $\frac{1}{81}$.

False.

Option (2)

$9^{-2}=\frac{1}{9^2}$

      $=\frac{1}{81}$

True.

Option (3)

$\frac{9^{8}}{9^{4}}=9^{(8-4)}$

    $=9^{4}$

    = 6561

False.

Option (4)

$\frac{9^8}{9^{10}}=9^{8-10}$

     $=9^{-2}$

     $=\frac{1}{81}$

True.

Option (5)

$9^{-6}9^{3}$ = $9^{-6+3}$

         = $9^{-3}$

         = $\frac{1}{9^3}$

         = $\frac{1}{729}$

False

Option (6)

$9^{5}9^{-7}=9^{(5-7)}}$

          $=9^{-2}$

          $=\frac{1}{9^2}$

           $=\frac{1}{81}$

True.

Therefore, Options (2), (4) and (6) are the correct options.

Answer 2

Applying the negative exponent rule of power, the expressions that are equivalent to the given expression, 1/81, are: B, D, and F.

What is the Negative Exponent Rule of Power?

The negative exponent rule states that: $a^{-n} = \frac{1}{a^n}$.

Thus, given the expression, 1/81, it can be rewritten or simplified as follows:

1/81 = $81^{-1} = 9^{-2}$ = $\frac{9^8}{9^{10}}$ = $9^5 \times 9^{-7}$

The expressions that will be equivalent to 1/81 can be expressed, based on the negative exponent rule of power, as:

$9^{-2}, \frac{9^8}{9^{10}} , 9^5 \times 9^{-7}$ (option B, D, and F).

Learn more about negative exponent rule on:

https://brainly.com/question/11975096

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