Question

select all the expressions that are equivalent to \\(\left(10^{4}\
ight)^{6}\\).\
\\(5^{24} \cdot 2^{24}\\) \\(10^{24}\\)\
\\(\frac{1}{10^{10}}\\) \\(\left(10^{6}\
ight)^{4}\\)

Explanation:

Step1: Simplify the original expression

$(10^4)^6 = 10^{4×6} = 10^{24}$

Step2: Check 5²⁴·2²⁴

$5^{24}·2^{24}=(5×2)^{24}=10^{24}$ (product rule of exponents)

Step3: Check 10²⁴

Directly matches the simplified original expression

Step4: Check 1/10¹⁰

$10^{-10}≠10^{24}$, so not equivalent

Step5: Check (10⁶)⁴

$(10^6)^4 =10^{6×4}=10^{24}$ (power of a power rule)

Answer:

10²⁴, 5²⁴·2²⁴, (10⁶)⁴