Question

evaluate (((256)^-1/2)^-1/4)^3​

Answer 1

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Answer 2

Answer:

The value of the given expression is 8.

Step-by-step explanation:

Given

${ { {(256)}^{( - \frac{1}{2}) } }^{( - \frac{1}{4}) } }^{3}$

First we are breaking 256,

$256 = 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2 \times 2$

Or,$256 = {2}^{8}$

Here

${ { {( {2}^{8} )}^{( - \frac{1}{2}) } }^{( - \frac{1}{4}) } }^{3} = { { {(2)}^{( 8 \times (- \frac{1}{2})) } }^{( - \frac{1}{4}) } }^{3} = { { {(2)}^{( - 4) } }^{( - \frac{1}{4}) } }^{3} = { { {(2)}^{( - 4 \times ( - \frac{1}{4} ) } }^{} }^{3} = { {2}^{1} }^{3} = {2}^{1 \times 3} = {2}^{3} = 2 \times 2 \times 2 = 8$

The value of the given expression is 8.

Here applied formula is

${( {a}^{p} )}^{q} = {a}^{p \times q}$

Some others formula of power and indices are

${x}^{p} \times {y}^{p} = {(xy)}^{p}$

$\frac{ {x}^{p} }{ {y}^{p} } = {( \frac{x}{y} )}^{p}$

${x}^{p} \times {x}^{q} = {x}^{p + q}$

$\frac{ {x}^{p} }{ {x}^{q} } = {x}^{p - q}$

${x}^{0} = 1$

${x}^{1} = x$