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4 years ago

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

Mathematics

2 answers:

Rudiy274 years ago

7 0

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.

uranmaximum [27]4 years ago

6 0

<span>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</span>

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