Mathematics, 12.09.2019 19:30, ssrt8771

Which of the following properties can be used to show that the expression 4^5/3 is equivalent to ^3√4^5

Which of the following properties can be used to show that the expression 4^5/3 is equivalent to ^3√

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answered: mariatorres7

First option.

Step-by-step explanation:

For this exercise it is importnatn to to remember the properties that are shown below:

1) $a^\frac{1}{n}=\sqrt[n]{a}$

2) $(a^m)^n=a^{(mn)}$

Therefore, given the following expression provided in the exercise:

$\sqrt[3]{4^5}$

You can apply the properties mentioned before, in order to find an equivalent expression.

Therefore, you get:

$\sqrt[3]{4^5}=(4^5)^{\frac{1}{3}}=4^{\frac{5*1}{3}}=4^{\frac{5}{3}}$

Then the answer is the first option.

answered: mesposito

$\sqrt[3]{4^5}=(4^5)^{\frac{1}{3}}=4^{\frac{5}{3}}$

Option 1 and Option 3 is correct

Step-by-step explanation:

Given: $4^{\frac{5}{3}}=\sqrt[3]{4^5}$

This is exponent to radical change property.

The fraction exponent write as radical.

$a^{\frac{m}{n}}=\sqrt[n]{a^m}$

Option 1: Radical to exponent

$\sqrt[3]{4^5}=(4^5)^{\frac{1}{3}}=4^{\frac{5}{3}}$

True

Option 2: Addition of exponent if base is same.

$4^{\frac{8}{3}}\cdot 4^{\frac{7}{3}}=4^{{\frac{8}{3}+\frac{7}{3}}=4^5$

False

Option 3: Multiply exponent to exponent, TrueOption 4: Division property of exponent, False

answered: Guest

hbfhv.hjgfskhgfdbmx n

step-by-step explanation:

9-15%

answered: Guest

(2 x^3 + 7 x^2 + 5 x + 2)/(x (x + 2))

step-by-step explanation:

simplify the following:

x/x^2 + 3 x + 2 - (x (x + 1))/(x + 2)

combine powers. x/x^2 = x^(1 - 2):

x^(1 - 2) + 3 x + 2 - (x (x + 1))/(x + 2)

1 - 2 = -1:

x^(-1) + 3 x + 2 - (x (x + 1))/(x + 2)

put each term in 1/x + 3 x + 2 - (x (x + 1))/(x + 2) over the common denominator x (x + 2): 1/x + 3 x + 2 - (x (x + 1))/(x + 2) = (x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)):

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2))

(x + 2)/(x (x + 2)) + (3 x^2 (x + 2))/(x (x + 2)) + (2 x (x + 2))/(x (x + 2)) - (x^2 (x + 1))/(x (x + 2)) = ((x + 2) + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2)):

(2 + x + 3 x^2 (x + 2) + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

3 x^2 (x + 2) = 3 x^3 + 6 x^2:

(2 + x + 3 x^3 + 6 x^2 + 2 x (x + 2) - x^2 (x + 1))/(x (x + 2))

2 x (x + 2) = 2 x^2 + 4 x:

(2 + x + 6 x^2 + 3 x^3 + 2 x^2 + 4 x - x^2 (x + 1))/(x (x + 2))

-x^2 (x + 1) = -x^2 - x^3:

(-x^2 - x^3 + 3 x^3 + 6 x^2 + 2 x^2 + 4 x + x + 2)/(x (x + 2))

grouping like terms, 3 x^3 - x^3 + 6 x^2 + 2 x^2 - x^2 + 4 x + x + 2 = (3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2:

((3 x^3 - x^3) + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

3 x^3 - x^3 = 2 x^3:

(2 x^3 + (6 x^2 + 2 x^2 - x^2) + (x + 4 x) + 2)/(x (x + 2))

6 x^2 + 2 x^2 - x^2 = 7 x^2: