Question

simlify[{(256)^-1/2}^-1/4]^2​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer:

4 is the required value of $[(256)^{\frac{-1}{2} }]^{\frac{-1}{4} }]^2$

Step-by-step explanation:

Explanation:

Given that, [$[(256)^{\frac{-1}{2} }]^{\frac{-1}{4} }]^2$]

• As we know, BEDMAS Brackets, exponents, division, multiplication, addition, and subtraction are an acronym representing the mathematical order of precedence, with B first and AS last.

• According to BEDMAS, exponents come in second, followed by both division and multiplication, then brackets, and finally addition and subtraction.

• As we know from the exponent's rule, $(a^m)^n = a^{m.n}$ is the power rule for exponents. Multiply the exponent by the power to raise a number with an exponent to that power.

Step 1:

We have,$[(256)^{\frac{-1}{2} }]^{\frac{-1}{4} }]^2$

As we know, powers are multiplied by each other after opening the brackets.

⇒$[(256)^{\frac{-1}{2} }]^{\frac{-1}{4} .(2)}$ = $[(256)^{\frac{-1}{2} }]^{\frac{-1}{2} }$

⇒$[(256)]^{\frac{-1}{2} .\frac{-1}{2} }$ = $[256]^{\frac{1}{4} }$

As we know that '-' × '-' = +

Now, 256 can be written as $(2)^8$.

[Where 2×2×2×2×2×2×2×2 = 256 = $2^8$]

Therefore, $[256]^{\frac{1}{4} } = [(2)^8]^{\frac{1}{4} }$

Now, on opening the bracket exponents multiply each other.

⇒$(2)^{8. \frac{1}{4} }$ = $(2)^2$ = 4

Final answer:

Hence, after solving it we get 4 as a result.

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