[tex]\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \boxed{2^{2x}=3}~\hspace{7em}4^{4x-3}\implies (2^2)^{4x-3}\implies 2^{2(4x-3)}\implies 2^{8x-6} \\\\\\ 2^{8x}\cdot 2^{-6}\implies \cfrac{2^{8x}}{2^6}\implies \cfrac{2^{4\cdot 2x}}{2^6}\implies \cfrac{(2^{2x})^4}{2^6}\implies \cfrac{(3)^4}{2^6}\implies \cfrac{81}{64}[/tex]
The value of [tex]4^{(4x-3)[/tex] the equation will be [tex]\frac{81 }{64}[/tex] .
Expressions is a finite combination of symbols that is well-formed according to rules that depend on the context.
We have,
[tex]2^{2x} =3[/tex]
And,
[tex]4^{(4x-3)} = 2^{2(4x-3)} =2^{{(8x-6)[/tex]
Now,
We have,
[tex]2^{{(8x-6)[/tex]
Now, Rewrite above expression,
[tex]2^{{(8x-6)\ =\ 2^{8x} *\ 2^{-6}[/tex]
Using the exponent rule,
i.e.
[tex]a^{-n}=\frac{1}{a^{n}}[/tex]
⇒
[tex]\ 2^{8x} *\ 2^{-6}[/tex]
[tex]=\frac{2^{8x} }{2^{6}}[/tex]
[tex]=\frac{2^{2x\ *\ 4} }{2^{6}}[/tex]
[tex]=\frac{2^{(2x) 4} }{2^{6}}[/tex]
And,
We have,
[tex]2^{2x} =3[/tex]
So,
Using this , we get,
[tex]=\frac{3^{ 4} }{2^{6}}[/tex]
[tex]=\frac{81 }{64}[/tex]
So,
[tex]4^{(4x-3)}=\frac{81 }{64}[/tex]
Hence, we can say that the value of [tex]4^{(4x-3)[/tex] the equation will be [tex]\frac{81 }{64}[/tex] .
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