Question

Which of the following shows the correct steps to find the value of 16 to the power of 1 over 4?

16 to the power of 1 over 4 equals 2 to the power of 4 to the power of 1 over 4 equals 2 to the power of 4 multiplied by 1 over 4 equals 2
16 to the power of 1 over 4 equals 4 to the power of 4 to the power of 1 over 4 equals 4 to the power of 4 multiplied by 1 over 4 equals 4
16 to the power of 1 over 4 equals 2 to the power of 8 to the power of 1 over 4 equals 8 to the power of 8 multiplied by 1 over 4 equals 4
16 to the power of 1 over 4 equals 8 to the power of 2 to the power of 1 over 4 equals 2 to the power of 2 multiplied by 1 over 4 equals 8

Answer 1

Ans.  16 to the power of 1 over 4 equals 4 to the power of 4 to the power of 1 over 4 equals 4 to the power of 4 multiplied by 1 over 4 equals 4

Answer 2

Answer:

Option A is correct.

Value of 16 to the power of 1 over 4 equals to the power of 4 to the power of 1 over 4 equals 2 to the power of 4 multiplies by 1 over 4 equal 2.

Step-by-step explanation:

To find the value of: 16 to the power of 1 over 4.

$16^{\frac{1}{4}}$

we can write 16 as:

$16 = 2 \cdot 2 \cdot 2 \cdot 2 = 2^4$

⇒$(2^4)^{\frac{1}{4}}$

⇒$(2)^{4 \cdot \frac{1}{4}}$             [∴$(a^n)^m = a^{nm}$]

⇒2

Hence, the value of $16^{\frac{1}{4}}$ is, 2.

Therefore, the value of 16 to the power of 1 over 4 equals to the power of 4 to the power of 1 over 4 equals 2 to the power of 4 multiplies by 1 over 4 equal 2.