To find an equivalent expression for \(1.1(1.3)^{x+4}\), let's carefully analyze the given expression and use the properties of exponents.
We have:
[tex]\[ 1.1(1.3)^{x+4} \][/tex]
One of the key properties of exponents is that \(a^{b+c} = a^b \cdot a^c\). Applying this property to the given expression, where \(a = 1.3\), \(b = x\), and \(c = 4\):
[tex]\[ (1.3)^{x+4} = (1.3)^x \cdot (1.3)^4 \][/tex]
So the expression \(1.1(1.3)^{x+4}\) can be rewritten as:
[tex]\[ 1.1 \cdot (1.3)^x \cdot (1.3)^4 \][/tex]
This matches with one of the given options. Specifically:
[tex]\[ 1.1(1.3)^4(1.3)^x \][/tex]
Therefore, the correct equivalent expression is:
[tex]\[ 1.1(1.3)^4(1.3)^x \][/tex]
In conclusion, the equivalent expression among the given options is:
[tex]\[ 1.1(1.3)^4(1.3)^x \][/tex]
