Question

order the expressions by choosing >, <, or =.
$3^{5} \times 3^{3} \quad \square \quad 3^{15}$
$3^{3} \times 5^{3} \quad \square \quad 15^{5}$
$3^{5} \times 5^{3} \quad \square \quad 15^{3}$

Explanation:

Step1: Simplify first expression

When multiplying exponents with the same base, add exponents: $3^5 \times 3^3 = 3^{5+3} = 3^8$. Compare to $3^{15}$: since $8 < 15$, $3^8 < 3^{15}$.

Step2: Simplify second expression

Rewrite $15^3$ as $(3 \times 5)^3 = 3^3 \times 5^3$. Compare to $15^5$: $3^3 \times 5^3 = 15^3$, and $3 < 5$, so $15^3 < 15^5$.

Step3: Simplify third expression

Rewrite $15^3$ as $(3 \times 5)^3 = 3^3 \times 5^3$. Compare to $3^5 \times 5^3$: factor out $5^3$, so we compare $3^5$ and $3^3$. Since $5 > 3$, $3^5 \times 5^3 > 3^3 \times 5^3 = 15^3$.

Answer:

$3^5 \times 3^3 < 3^{15}$
$3^3 \times 5^3 < 15^5$
$3^5 \times 5^3 > 15^3$