Question

select all the expressions that are equivalent to $10^{6} \cdot 3^{6}$.
$\frac{1}{30^{6}}$
$30^{12}$
$30^{6}$
$30^{36}$

Explanation:

Step1: Recall exponent product rule

For $a^n \cdot b^n = (a \cdot b)^n$

Step2: Apply rule to given expression

$10^6 \cdot 3^6 = (10 \times 3)^6 = 30^6$

Step3: Evaluate other options

• $\frac{1}{30^6} = 30^{-6}

eq 30^6$

• $30^{12} = (30^6)^2

eq 30^6$

• $30^{36} = (30^6)^6

eq 30^6$

Answer:

$30^6$