To find an expression that is equivalent to [tex]\(2^{3x - 4}\)[/tex], we can use properties of exponents to rewrite the given expression in a different form.
First, recall the property of exponents which states:
[tex]\[a^{b - c} = \frac{a^b}{a^c}\][/tex]
Applying this property, we consider [tex]\(a = 2\)[/tex], [tex]\(b = 3x\)[/tex], and [tex]\(c = 4\)[/tex]. This allows us to rewrite the expression [tex]\(2^{3x - 4}\)[/tex] as:
[tex]\[2^{3x - 4} = \frac{2^{3x}}{2^4}\][/tex]
Next, we need to evaluate [tex]\(2^4\)[/tex]. When we calculate this, we get:
[tex]\[2^4 = 16\][/tex]
Substituting this value back into our expression, we get:
[tex]\[2^{3x - 4} = \frac{2^{3x}}{16}\][/tex]
Hence, the expression that is equivalent to [tex]\(2^{3x - 4}\)[/tex] is:
[tex]\[\frac{2^{3x}}{16}\][/tex]
