Question

Please I need help with this!!!!!!!

Answer 1

1). Step 4:

x=5^{\frac{4}{3}}=(5^4)^{\frac{1}{3}}x=534=(54)31

x=\sqrt[3]{5^4}x=354 [Since, a^{\frac{1}{3}}=\sqrt[3]{a}a31=3a

x=\sqrt[3]{5\times 5\times 5\times 5}x=35×5×5×5

Step 5:

x=\sqrt[3]{(5)^3\times 5}x=3(5)3×5

x=\sqrt[3]{5^3}\times \sqrt[3]{5}x=353×35

2). He simplified the expression by removing exponents from the given expression.

3). Let the radical equation is,

(3x-1)^{\frac{1}{5}}=2(3x−1)51=2

Step 1:

(3x-1)^{\frac{1}{5}\times \frac{5}{1} }=2^{\frac{5}{1}}(3x−1)51×15=215

Step 2:

(3x-1)=2^5(3x−1)=25

Step 3:

3x=32+13x=32+1

Step 4:

x=11x=11

4). By substituting x=11x=11 in the original equation.

(3\times 11-1)^{\frac{1}{5}}=(32)^\frac{1}{5}(3×11−1)51=(32)51

=(2^5)^\frac{1}{5}=(25)51

=2=2

There is no extraneous solution.

Answer 2

Explanation:

1). Step 4:

`x=5^{(4)/(3)}=(5^4)^{(1)/(3)}`

`x=\sqrt[3]{5^4}` [Since,
`a^{(1)/(3)}=\sqrt[3]{a}`]

`x=\sqrt[3]{5* 5* 5* 5}`

Step 5:

`x=\sqrt[3]{(5)^3* 5}`

`x=\sqrt[3]{5^3}* \sqrt[3]{5}`

2). He simplified the expression by removing exponents from the given expression.

3). Let the radical equation is,

`(3x-1)^{(1)/(5)}=2`

Step 1:

`(3x-1)^{(1)/(5)* (5)/(1) }=2^{(5)/(1)}`

Step 2:

`(3x-1)=2^5`

Step 3:

`3x=32+1`

Step 4:

`x=11`

4). By substituting
`x=11` in the original equation.

`(3* 11-1)^{(1)/(5)}=(32)^(1)/(5)`

`=(2^5)^(1)/(5)`

`=2`

There is no extraneous solution.