Consider the expression [tex]1.1(1.3)^{x+4}[/tex]. Which of the following is an equivalent expression?

A. [tex]1.1(1.3)^{4x}[/tex]

B. [tex]1.1(13)^{\frac{x}{4}}[/tex]

C. [tex]\frac{1.1(1.3)^x}{1.3^4}[/tex]

D. [tex]1.1(1.3)^4(1.3)^x[/tex]



Answer :

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]