Solve Fifth Root Expression: Multiplying ∛(3³) and ∛(3²)
Question
Solve the following exercise:
533⋅532=
Video Solution
Solution Steps
00:00Simplify the following expression
00:03The C root of the A value to the power of B
00:06The result will be equal to number A to the power of B divided by C
00:10We will use this formula in our exercise
00:14When multiplying powers with equal bases
00:17The power of the result equals the sum of the powers
00:21We will use this formula in our exercise, and add the powers
00:36This is the solution
Step-by-Step Solution
In order to simplify the given expression, we will apply two laws of exponents:
a. The root law (expanded):
nam=anm=(na)m
b. The law of exponents for multiplication between terms with identical bases:
am⋅an=am+n
Begin by converting the roots to exponent notation using the law of exponents mentioned in a:
533⋅532=↓353⋅352=
Given that we are multiplying two terms with identical bases, we'll apply the law of exponents mentioned in b:
353⋅352=353+52=
Proceed to perform the addition of fractions in the exponent of the expression separately. We can achieve this by expanding each of the fractions to the common denominator—the number 5—then we'll perform the multiplication and addition operations in the fraction numerator:
53+52=53+2=55=1
We obtain the following:
353+52=31=3
Let's summarize the expression simplification process: