Question

Which expressions are equivilant to 6^16?

Answer 1

The expressions which are equivalent to 6¹⁶ are

$(6^{8}) ^{2}$

$(6^{-2}) ^{\times -8}$

and $(6^{-4}) ^{\times -4}$

Equivalent expressions

From the question, we are to determine which of the given expressions are equivalent to 6¹⁶

From one of the laws of indices, we have that

$x^{y\times z} = (x^{y})^{z}$

The given expression, 6¹⁶, can be expressed as

$6^{8\times 2}$

or

$6^{-2\times -8}$

or

$6^{-4\times -4}$

Then,

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

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

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

Hence, the expressions which are equivalent to 6¹⁶ are

$(6^{8}) ^{2}$

$(6^{-2}) ^{\times -8}$

and $(6^{-4}) ^{\times -4}$

Learn more on Equivalent expressions here: brainly.com/question/21643960

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