Question

How to solve 16 raise to power 1/4

Answer 1

2 is the right answer...
hope this helps you....

Answer 2

Given:

Exponent is $\mathbf{ (16)^{\dfrac{1}{4}}}$

To Find:

What is value of exponent $\mathbf{ (16)^{\dfrac{1}{4}}}$ ?

Solution:

16 can be written as prime factorization of 2 as:

16 = 2 ×2 ×2 ×2

Here all base of multiplication is 2, so we can do algebraic addition of exponent:

$\mathbf{ 16 = 2^{1+1+1+1}}$

So:

$\mathbf{ 16 = 2^{4}}$                 ...1)

We also know the formula:

$\mathbf{(a^{n})^{m}=a^{n\times m}}$      ...2)

Now come to question:

$\mathbf{ The \ value \ of \ exponent= (16)^{\dfrac{1}{4}}}$

R.H.S of above equation can be write with help of equation 1):

$\mathbf{ The \ value \ of \ exponent= (2^{4})^{\dfrac{1}{4}}}}$

R.H.S of above equation can be write with help of equation 2):

$\mathbf{ The \ value \ of \ exponent= (2)^{4\times \dfrac{1}{4}}}}$

After solving the exponent of 2:

$\mathbf{ The \ value \ of \ exponent= (2)^{1}}$

$\mathbf{(16)^{\dfrac{1}{4}}=2}$

The value of $\mathbf{ (16)^{\dfrac{1}{4}}}$ is 2.