To solve the expression [tex]\(3^{2x + 3}\)[/tex] when [tex]\(x = 1\)[/tex], follow these steps:
1. Substitute the value of [tex]\(x\)[/tex] into the expression:
Given [tex]\(x = 1\)[/tex], replace [tex]\(x\)[/tex] in the expression [tex]\(3^{2x + 3}\)[/tex]:
[tex]\[
3^{2(1) + 3}
\][/tex]
2. Simplify the exponent:
Calculate [tex]\(2(1) + 3\)[/tex]:
[tex]\[
2 \times 1 + 3 = 2 + 3 = 5
\][/tex]
3. Evaluate the expression with the simplified exponent:
The expression now becomes:
[tex]\[
3^5
\][/tex]
4. Calculate the value of [tex]\(3^5\)[/tex]:
[tex]\(3^5\)[/tex] means [tex]\(3\)[/tex] multiplied by itself [tex]\(5\)[/tex] times:
[tex]\[
3 \times 3 \times 3 \times 3 \times 3 = 243
\][/tex]
Hence, [tex]\(3^{2x + 3}\)[/tex] evaluates to [tex]\(243\)[/tex] when [tex]\(x = 1\)[/tex].
