To break down the given expression [tex]\(300(4)^{x+3}\)[/tex] and determine which option it is equivalent to, follow these steps:
1. Rewrite the expression using properties of exponents:
- The given expression is [tex]\(300(4)^{x+3}\)[/tex].
- We recall the exponent rules: [tex]\(a^{b+c} = a^b \cdot a^c\)[/tex]. This allows us to split the exponent addition into multiplication of individual exponents.
2. Apply the exponent rules:
- Rewrite [tex]\((4)^{x+3}\)[/tex] as [tex]\((4)^x \cdot (4)^3\)[/tex].
- Substitute this back into the original expression:
[tex]\[
300(4)^{x+3} = 300 \cdot (4)^x \cdot (4)^3
\][/tex]
3. Further simplify the expression:
- We observe that there is no further simplification needed. Therefore, the expression [tex]\(300(4)^{x+3}\)[/tex], when simplified, becomes [tex]\(300 (4)^x (4)^3\)[/tex].
4. Match the simplified expression to the given options:
- Option (1) is [tex]\(300(4)^x(4)^3\)[/tex].
- This exactly matches our simplified expression.
Thus, the expression [tex]\(300(4)^{x+3}\)[/tex] is equivalent to [tex]\(\boxed{300(4)^x(4)^3}\)[/tex]. Therefore, the correct answer is:
[tex]\[
\boxed{1}
\][/tex]
