Question

select all the expressions that are equivalent to $3^3 \cdot 5^3$.
$\frac{1}{15^3}$
$15^9$
$\frac{1}{15^{-3}}$
$15^6$

Explanation:

Step1: Simplify the original expression

Use exponent rule $a^n \cdot b^n=(a\cdot b)^n$:
$3^3 \cdot 5^3=(3\cdot5)^3=15^3$

Step2: Evaluate each option

• Option 1: $\frac{1}{15^3}=15^{-3}

eq 15^3$

• Option 2: $15^9

eq 15^3$

• Option 3: $\frac{1}{15^{-3}}=15^{3}$ (using $\frac{1}{a^{-n}}=a^n$)
• Option 4: $15^6

eq 15^3$

Answer:

$\frac{1}{15^{-3}}$