Question

What is the value of (16)³/⁴

Answer 1

Answer:

${16}^{3 \div 4} \\ {2}^{4 \times 3 \div 4 } \\ {2}^{3 } \\ = 8$

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Answer 2

Answer:

$8$

Step-by-step explanation:

We know that power is simply a type of expression. It is used to represent the repeated (one after the other) multiplication of an integer.

In the expression $N^{a}$:

• $N^{a}$ is the power.
• $a$ is the exponent.

Given: $16^{\frac{3}{4} }$

Solution: $16^{\frac{3}{4} }$ can also be written as $(2^{4} )^{\frac{3}{4} }$

According to the law of exponents, $(a^{m} )^{n} = a^{mn}$

In the given question,

• $a = 2$
• $m = 4$
• $n = \frac{3}{4}$

Putting these values in the above equation, we will get:

⇒ $(2^{4} )^{\frac{3}{4} }$

⇒ $2^{4 \times \frac{3}{4} }$

⇒ $2^{\frac{12}{4} }$

⇒ $2^{3}$

⇒ $2 \times 2 \times 2$

⇒ $8$

Hence, the value of $16^{\frac{3}{4} }$ is $8$.

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