which expression is equivalent to (x^4/3*x^2/3)^1/3
Mathematics · High School · Mon Jan 18 2021
Answered on
Given the expression:
((x^4/3) (x^⅔))^⅓
Determine the equivalent expression.
Solution:
In order to determine the equivalent expression, we must simply apply the laws of exponent, involving multiplying exponents, and enclosing an exponent with another degree.
(a^n)(a^m) = a^(n + m)
In multiplying two exponents with the same base, we simply add the exponents together.
((a^n)^m = a^nm
In raising an exponent with another exponent, we simply needed to multiply the exponents.
= ((x^4/3) (x^⅔))^⅓
= ((x^(4/3 + ⅔))^⅓
= ((x^2)^⅓
= x^((2)(⅓))
= x^⅔
Final answer:
= x^⅔