Final answer:
The expression (√3)(√3)(√5 3) simplifies to 3^(7/10), after adding the exponents of the same base and converting them to a common denominator of 10, which is the tenth root of 3 raised to the seventh power.
Step-by-step explanation:
The question asks to simplify the expression (√3)(√3)(√53).
First, let's recall that (√3) is the same as 31/2. We are also given (√53), which can be written as 31/5. When we multiply expressions with the same base, we add the exponents. Thus, simplifying the given expression would mean adding the exponents of 3, which are 1/2 and 1/5.
The combined exponent is 1/2 + 1/5. To add these fractions, we need a common denominator, which would be 10. Convert each fraction to an equivalent fraction with a denominator of 10: 5/10 + 2/10, which equals 7/10. The simplified expression would thus be 37/10.
So, (√3)(√3)(√53) simplifies to 37/10, or in radical form, the 10th root of 3 raised to the 7th power.