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never [62]
3 years ago
8

Which expressions are equivalent to R16? Check all that apply.

Mathematics
1 answer:
Ilya [14]3 years ago
6 0

Option C:  (6^{-4})^{-4}

Option D:  (6^{-2})^{-8}

Option F:  (6^8)^2

Solution:

Given expression: 6^{16}

To find which expression is equivalent to the given expression.

Let us solve this using exponent rule: \left(a^{b}\right)^{c}=a^{b c}

Option A: (6^{0})^{16}

(6^{0})^{16}=6^{0 \times 16}= 6^0

It is not equivalent expression.

Option B: (6^8)^8

(6^{8})^{8}=6^{8 \times 8}= 6^{64}

It is not equivalent expression.

Option C:  (6^{-4})^{-4}

(6^{-4})^{-4}=6^{(-4 )\times (-4)}= 6^{16}

It is equivalent expression for the given expression.

Option D:  (6^{-2})^{-8}

(6^{-2})^{-8}=6^{(-2) \times (-8)}= 6^{16}

It is equivalent expression for the given expression.

Option E:  (6^{-1})^{16}

(6^{-1})^{16}=6^{(-1) \times 16}= 6^{-16}

It is not equivalent expression.

Option F:  (6^8)^2

(6^{8})^{2}=6^{8 \times 2}= 6^{16}

It is equivalent expression for the given expression.

Hence (6^{-4})^{-4}, \ (6^{-2})^{-8}, \ (6^8)^2 are the equivalent expressions.

Option C, Option D and Option F are correct answers.

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