Question

{(125)²×(8)÷(64)²}1÷3​

Answer 1

Step-by-step explanation:

Solution-

Given expression,

$\left[{ \frac{(125 {)}^{2} \times (8)}{(64 {)}^{2} } }\right] ^{1/3}$

Calculate 125 to the power of 2 and get 15625.

$\longrightarrow \: \bigg(\frac{15625 \times 8}{64 ^{2} } \bigg)^{1/3}$

Multiply 15625 and 8 to get 125000.

$\longrightarrow \: \bigg(\frac{125000}{64 ^{2} } \bigg)^{1/3}$

Calculate 64 to the power of 2 and get 4096.

$\longrightarrow \: \bigg(\frac{125000}{4096} \bigg)^{1/3}$

Reduce the fraction 125000/512 to the lowest terms by extracting and cancaling out 8.

$\longrightarrow \: \bigg(\frac{15625}{512} \bigg)^{1/3}$

Calculate 15625/512 to the power of ⅓ and get 25/8.

$\longrightarrow \: \boxed{ \frac{25}{8} = 3.125}$

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