Question

find the value of 4√16^-2​

Answer 1

Answer:

the answer is 4^-1.

Step-by-step explanation:

• 4(16)^(1/2×-2)
• 4(4)^2×-1
• 4^-1
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Answer 2

$\displaystyle \sf \sqrt[4]{ {16}^{ - 2} } = \bf \frac{1}{4}$

Given :

$\displaystyle \sf \sqrt[4]{ {16}^{ - 2} }$

To find :

The value of the expression

Solution :

Step 1 of 2 :

Write down the given expression

Here the given expression is

$\displaystyle \sf \sqrt[4]{ {16}^{ - 2} }$

Step 2 of 2 :

Find the value of the expression

$\displaystyle \sf \sqrt[4]{ {16}^{ - 2} }$

$\displaystyle \sf = \sqrt[4]{ \frac{1}{ {16}^{2} } }$

$\displaystyle \sf = \sqrt[4]{ \frac{1}{ 16 \times 16 } }$

$\displaystyle \sf = \sqrt[4]{ \frac{1}{ (2 \times 2 \times 2 \times 2) \times (2 \times 2 \times 2 \times 2) } }$

$\displaystyle \sf = \sqrt[4]{ \frac{1}{ {2}^{4} \times {2}^{4} } }$

$\displaystyle \sf = \sqrt[4]{ \frac{1}{ {(2 \times 2)}^{4} } }$

$\displaystyle \sf = \sqrt[4]{ \frac{1}{ {4}^{4} } }$

$\displaystyle \sf = {\bigg( \frac{1}{ {4}^{4} } \bigg)}^{ \frac{1}{4} }$

$\displaystyle \sf = \frac{1}{4}$

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