Question

(а^(5/3):а^(1/3) )*∛(а^2 )

Answer 1

(а^(5/3):а^(1/3) )*∛(а^2 ) = a^(5/3 - 1/3 + 2/3) = a^2

Answer 2

За свойствами корней:

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

Когда делим, отнимаем; когда умножаем, прибавляем.

Получается:

$\frac{5}{3} - \frac{1}{3} + \frac{2}{3} = \frac{6}{3} = 2$

Итог:

$a^{2}$

Answer 3

To simplify the given expression, we can use the properties of exponents. Remember that when you divide two numbers with the same base, you subtract the exponents. Also, when you take the cube root of a number raised to an exponent, you divide the exponent by 3. Let's simplify the expression step by step:

Expression: (a^(5/3) : a^(1/3)) * ∛(a^2)

Step 1: Simplify the division of exponents. a^(5/3) : a^(1/3) = a^(5/3 - 1/3) = a^(4/3)

Step 2: Simplify the cube root of a^2. ∛(a^2) = a^(2/3)

Now, the expression becomes: a^(4/3) * a^(2/3)

Step 3: Apply the property of multiplication of exponents with the same base. When you multiply two numbers with the same base, you add the exponents. a^(4/3) * a^(2/3) = a^(4/3 + 2/3) = a^(6/3)

Step 4: Simplify the exponent. a^(6/3) = a^2

So, the simplified expression is just a^2.