Answer:
The given expression is equivalent to [tex](\sqrt[4]{16})^{3x}[/tex] or [tex]8^x[/tex].
Step-by-step explanation:
The given expression is
[tex]16^{\frac{3}{4}x}[/tex]
Use the property of exponent ,
[tex]x^{mn}=(x^m)^n[/tex]
[tex]16^{\frac{3}{4}x}=(16^\frac{1}{4})^{3x}[/tex]
Use the property of radical expression,
[tex]x^{\frac{1}{n}}=\sqrt[n]{x}[/tex]
[tex]16^{\frac{3}{4}x}=(\sqrt[4]{16})^{3x}[/tex]
Therefore the given expression is equivalent to [tex](\sqrt[4]{16})^{3x}[/tex].
After more simplification we get,
[tex]16^{\frac{3}{4}x}=2^{3x}[/tex]
[tex]16^{\frac{3}{4}x}=8^x[/tex]
Therefore the given expression is also equivalent to [tex]8^x[/tex].
