Question

Evaluate.
Answer is 1/49 but I need solution. Most satisfying answer will mark as brainliest.
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Answer 1

Answer:

1/49

Step-by-step explanation:

given,

cube rt (343)^-2

(343)^(-2/3)

but 7^3=343

(7^3)^(-2/3)

(7^-2)

1/7^2

1/49

Answer 2

Answer:

$\Large \dfrac{1}{49}$

Step-by-step explanation:

We have to evaluate $\large \text{ \sqrt[3]{(343)^{-2}} }$

$\large Rewrite \ 343 \ as \ 7^3$

$\large \text{ \sqrt[3]{(343)^2} \implies\sqrt[3]{(7^3)^{-2}} }$

We know that any exponent function are always equal as

$\Large \text{ \sqrt[n]{x}=x^{\frac{1}{n} } }$

$\Large \text{ \sqrt[3]{(7^3)^{-2}} \implies {(7^{3\times-2\times\frac{1}{3}})} }\\\\\\\Large \text{ \implies {(7^{-2})} }$

we know that  $\Large y^{-1}=\dfrac{1}{y}$

Appying that we get

$\Large \text{ \implies {(7^{-2})} }\\\\\\\Large \implies \dfrac{1}{7^2} \\\\\\\Large \implies \dfrac{1}{49}$

Thus we get answer.