Question

select all the expressions that are equivalent to $10 \cdot 10^{2}$.
$5^{3} \cdot 2^{3}$
$\frac{1}{10^{2}}$
$10^{2}$
$(10^{3})^{1}$

Explanation:

Step1: Calculate target expression

$10 \cdot 10^2 = 10^{1+2} = 10^3 = 1000$

Step2: Evaluate first option

$5^3 \cdot 2^3 = (5 \cdot 2)^3 = 10^3 = 1000$

Step3: Evaluate second option

$\frac{1}{10^2} = 10^{-2} = 0.01$

Step4: Evaluate third option

$10^2 = 100$

Step5: Evaluate fourth option

$(10^3)^1 = 10^{3 \cdot 1} = 10^3 = 1000$

Answer:

$5^3 \cdot 2^3$, $(10^3)^1$