Question

Identify the value of the variable in the equivalent expressions.

Answer 1

The value of expression is n=3 and r= 16

What is expression?

An expression is a set of terms combined using the operations +, – , x or , /.

Given:

$(4k^{7})^{3} = 4^{n}* (k^{7})^{3} = 64 k^{21}$

$(64 k^{21}) = 4^{n}* k^{21} = 64 k^{21}$

$4 ^{3} * k^{21}= 4^{n}* k^{21}$

On comparing

n=3

Now,

$(-3r^{-4})^{-4} = (-3)^{-4} * (r^{-4})^{-4} = 1/81* r^{m}$

$(-3)^{-4} * (r^{-4})^{-4} = 1/81* r^{m}\\1/ (-3)^{4} * 1/(r^{-4})^{4} = 1/81* r^{m}\\1/ (-3)^{4} * (r^{16}) = 1/81* r^{m}$

1/81 * r^16 = 1/81 * r^{m}

On compairing

r = 16.

Learn more about this expression here:

brainly.com/question/13947055

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