Question

Identify the equivalent expression for each of the expressions below. Root(5, (m + 2) ^ 3). Root(3, (m + 2) ^ 5). Root(5, m ^ 3) + 2. Root(3, m ^ 5) + 2

Answer 1

Answer:

1. $(\sqrt[5]{(m+2)})^{3} = (m+2)^{\frac{3}{5}}$

2. $(\sqrt[3]{(m+2)})^{5} = (m+2)^{\frac{5}{3}}$

3. $\sqrt[5]{(m)}^{3}+2 = m^{\frac{3}{5}}+2$

4. $\sqrt[3]{(m)}^{5}+2 = m^{\frac{5}{3}}+2$

Step-by-step explanation:

Recall that

$(\sqrt[n]{x})^{m} = (x^{\frac{m}{n}})$

Where $x^{m}$ is called radicand and n is called index

1. Root(5, (m + 2) ^ 3)

In this case,

n is 5

m is 3

x = (m + 2)

$(\sqrt[5]{(m+2)})^{3} = (m+2)^{\frac{3}{5}}$

2. Root(3, (m + 2) ^ 5)

In this case,

n is 3

m is 5

x = (m + 2)

$(\sqrt[3]{(m+2)})^{5} = (m+2)^{\frac{5}{3}}$

3. Root(5, m ^ 3) + 2

In this case,

n is 5

m is 3

x = m

$\sqrt[5]{(m)}^{3}+2 = m^{\frac{3}{5}}+2$

4. Root(3, m ^ 5) + 2

In this case,

n is 3

m is 5

x = m

$\sqrt[3]{(m)}^{5}+2 = m^{\frac{5}{3}}+2$