How do we write #(sqrt7)^3# in exponential form?

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How do we write #(sqrt7)^3# in exponential form?

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Answer 1 · 2016-07-20T04:03:52

#(sqrt7)^3=7^(3/2)#

Explanation:

To write #(sqrt7)^3# in exponential form, one needs two identities - #root(n)a=a^(1/n)# and #(a^m)^n=a^((m×n))# which is true for all rational #m# and #n#.

Hence, #(sqrt7)^3#

= #(7^(1/2))^3#

= #7^((1/2×3))#

= #7^(3/2)#

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How do we write #(sqrt7)^3# in exponential form?

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