Question

Write (4√81)^6 in exponential form.

Answer 1

`\huge\textsf{Hey there!}`

`\mathsf{(4*√(81))^6}\\\\\mathsf{√(81) = \bf 9}\textsf{ because half of \underline{81} is \underline{9} or 9 multiplied by itself gives you 81}\\\\\mathsf{= (4*9)^6}\\\\\mathsf{4*9 = \bf 36}\\\\\mathsf{36^6}\\\mathsf{= 36*36*36*36*36*36}\\\mathsf{= 1,296*1,296*1,296}\\\mathsf{= 1,679,616*1,296}\\\mathsf{= \bf 2,176,782,336\ also\ known\ as \ 6^(12)}\\\\\\\boxed{\boxed{\large\textsf{Answer: \bf 6}^(\bf 12)}}\huge\checkmark`

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Answer 2

Explanation:

`(4√(81))^(6) = (4*√(9*9) )^(6)\\\\=(4*9)^(6)\\\\=(2^(2)*3^(2))^(6)\\\\=[(2*3)^(2)]^(6)\\\\=(6)^(2*6)\\\\=6^(12)`

Exponent Laws:

`(a^(m)*b^(m)) = (a*b)^(m)\\\\(a^(m))^(n)=a^(m*n)`