Question

simplify. assume all variables are positive.
$(49w)^{\frac{1}{2}}$
write your answer in the form $a$ or $\frac{a}{b}$, where $a$ and $b$ are constants or variable expressions that have no variables in common. all exponents in your answer should be positive.

Explanation:

Step1: Apply exponent product rule

$(ab)^\frac{1}{2}=a^\frac{1}{2}b^\frac{1}{2}$
So, $(49w)^\frac{1}{2}=49^\frac{1}{2} \cdot w^\frac{1}{2}$

Step2: Simplify constant term

$49^\frac{1}{2}=\sqrt{49}=7$
So, $49^\frac{1}{2} \cdot w^\frac{1}{2}=7w^\frac{1}{2}$

Step3: Rewrite to positive exponent form

$w^\frac{1}{2}=\sqrt{w}$, so the simplified form is $7\sqrt{w}$

Answer:

$7\sqrt{w}$