Question

question use the properties of exponents to determine the value of ( a ) for the equation below given ( x > 0 ). ( left(x^{2}
ight)^{\frac{1}{3}} sqrt3{x^{2}} = x^{a} ) watch video show examples answer attempt 2 out of 2

Explanation:

Step1: Rewrite root as exponent

$\sqrt[3]{x^2} = x^{\frac{2}{3}}$

Step2: Apply power of a power rule

$(x^2)^{\frac{1}{3}} \cdot x^{\frac{2}{3}} = x^{2 \cdot \frac{1}{3}} \cdot x^{\frac{2}{3}} = x^{\frac{2}{3}} \cdot x^{\frac{2}{3}}$

Step3: Apply product of powers rule

$x^{\frac{2}{3}} \cdot x^{\frac{2}{3}} = x^{\frac{2}{3} + \frac{2}{3}} = x^{\frac{4}{3}}$

Answer:

$\frac{4}{3}$