Question

Simplify (16)1/4*4root 16

Answer 1

Answer:

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Answer 2

The value of $16^{1/4}*\sqrt[4]{16}$ is 4.

Given,

An expression $16^{1/4}*\sqrt[4]{16}$.

To Find,

The value of this expression.

Solution,

The given expression is

$16^{1/4}*\sqrt[4]{16}$

Now, we know that

$\sqrt[4]{16} = 16^{1/4}$

So, the expression becomes

$16^{1/4}*16^{1/4}$

Using the identity, In the case of multiplication when bases are the same powers are added.

xᵃ*xᵇ = x⁽ᵃ⁺ᵇ⁾

$16^{1/4}*16^{1/4} = 16^{(1/4+1/4)} = 16^{1/2}$

$16^{1/2} = \sqrt{16}$

Now, the value of √16 = 4

Hence, the value of $16^{1/4}*\sqrt[4]{16}$ is 4.

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