Question

What is the value of the expression below? (9^2) ^1/4

Answer 1

Answer:

3

Step-by-step explanation:

1. Note that $9=3^2.$

2. Use property $(a^m)^n=a^{m\cdot n},$ then

$9^2=(3^2)^2=3^{2\cdot 2}=3^4.$

3. Use the same property, thus

$(9^2)^{\frac{1}{4}}=(3^4)^{\frac{1}{4}}=3^{4\cdot \frac{1}{4}}=3^1=3.$

Answer 2

ANSWER

3

EXPLANATION

The given expression is

${(9}^{2} )^{ \frac{1}{4} }$

Recall and use the property:

$({a}^{m})^{n} = {a}^{mn}$

$= {(9})^{ 2 \times \frac{1}{4} }$

$= {9}^{ \frac{1}{2} }$

$= \sqrt{9}$

$= 3$