(x) Simplify $$ 3^{2} \cdot 3^{5} \cdot 3^{-3} $$ A $$ 3^{-4} $$ B $$ 3^{4} $$ C $$ 3^{-10} $$ D $$ 3^{10} $$

Question

UpStudy AI · Accepted Answer

We are given the expression:

$$
3^{2} \cdot 3^{5} \cdot 3^{-3}
$$

Since the bases are the same, we can add the exponents. That is, for any real number $$a$$ and exponents $$m$$ and $$n$$:

$$
a^m \cdot a^n = a^{m+n}
$$

Applying this rule:

$$
3^{2} \cdot 3^{5} \cdot 3^{-3} = 3^{2+5+(-3)} = 3^{2+5-3} = 3^{4}
$$

Thus, the simplified expression is:

$$
3^{4}
$$

The correct answer is $$ \textbf{B} $$.
The simplified expression is $$ 3^{4} $$, which is choice B.

(x) Simplify \[ 3^{2} \cdot 3^{5} \cdot 3^{-3} \] A \( 3^{-4} \) B \( 3^{4} \) C \( 3^{-10} \) D \( 3^{10} \)