Respuesta :
Answer:
f(x) = [tex]4^{(\sqrt[3]{64} )^{2x}}[/tex].
Step-by-step explanation:
We are given functions
[tex]f(x) = 2^{(\sqrt[3]{16} )}[/tex]
f(x) = [tex]2^{(\sqrt[3]{64} )}[/tex]
f(x) = [tex]4{(\sqrt[3]{12})^{2x}}[/tex]
f(x) = [tex]4^{(\sqrt[3]{64} )^{2x}}[/tex].
We need to find the function with simplified base of 4.
Let us simplify each of the function one by one.
On simplifying exponent in[tex]2^{(\sqrt[3]{16} )}[/tex], we get [tex]2^{(2\sqrt[3]{2} )}[/tex].
On simplifying exponent in [tex]2^{(\sqrt[3]{64} )}[/tex] we get 2^{4}.
On simplifying [tex]4{(\sqrt[3]{12})^{2x}}[/tex] we get [tex]4\left(\sqrt[3]{12}\:\:\right)\left(\sqrt[3]{12}\:\:\right)^x=4\left(\sqrt[3]{12\cdot 12}\right)\:^x=4\left(2\sqrt[3]{18}\right)^x[/tex].
On simplifying [tex]4^{(\sqrt[3]{64} )^{2x}}[/tex] we get [tex]4^{\left(\sqrt[3]{64}\:\right)^{2x}}=4^{\left(4\:\right)^{2x}}=\:4^{16^x}.[/tex]
Therefore, fourth function f(x) = [tex]4^{(\sqrt[3]{64} )^{2x}}[/tex] has simplified base 4.
Answer:
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Step-by-step explanation:
