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PilotLPTM [1.2K]
3 years ago
12

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
Mathematics
1 answer:
vesna_86 [32]3 years ago
6 0

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

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