Question

Please help mee pleaseee

Answer 1

The exact answer in terms of radicals is
`x = 5*\sqrt[3]{25}`

The approximate answer is
`x \approx 14.62009` (accurate to 5 decimal places)

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Work Shown:

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

So the equation reduces to -7 = 8-3y

Let's solve for y

-7 = 8-3y

8-3y = -7

-3y = -7-8 ... subtract 8 from both sides

-3y = -15

y = -15/(-3) ... divide both sides by -3

y = 5

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Since
`y = \sqrt[5]{x^3}` and y = 5, this means we can equate the two expressions and solve for x

`y = 5`

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

`x^3 = 5^5` Raise both sides to the 5th power

`x^3 = 3125`

`x = \sqrt[3]{3125}` Apply cube root to both sides

`x = \sqrt[3]{125*25}`

`x = \sqrt[3]{125}*\sqrt[3]{25}`

`x = \sqrt[3]{5^3}*\sqrt[3]{25}`

`x = 5*\sqrt[3]{25}`

`x \approx 14.62009`

Answer 2

x = 14.62 (Rounding to two decimal places)

Explanation:

Let's solve for x, this way:

- 7 = 8 - 3 ⁵√x³

- 15 = - 3 ⁵√x³ (Subtracting 8 at both sides)

5 = ⁵√x³ (Dividing by - 3 at both sides)

5 ⁵ = x³(Raising both sides to the 5th power)

3,125 = x³

x = ∛ 3,125 (Cube root to both sides)

x = 14.62 (Rounding to two decimal places)