Question

RATIONAL EXPONENTS pls help what do i do??

Answer 1

x = 3

Explanation:

• 
  `26=-1+(27x)^{(3)/(4)}`

• 
  `\implies 26+1=27^{(3)/(4)} x^{(3)/(4)}`

• 
  `\implies 27/ 27^{(3)/(4)} =x^{(3)/(4)}`

• 
  `\implies 27^{1-(3)/(4)} =x^{(3)/(4)}`

• 
  `\implies 27^{(4-3)/(4)} =x^{(3)/(4)}`

• 
  `\implies 27^{(1)/(\cancel 4)} =x^{(3)/(\cancel 4)}`

• 
  `\implies 27 =x^(3)`

• 
  `\implies 27^{(1)/(3)} =x`

• 
  `\implies (3^3)^{(1)/(3)} =x`

• 
  `\implies x = 3`

Answer 2

x = 3

Explanation:

`26=-1+\left( 27x\right)^{(3)/(4) }`

`\Longleftrightarrow 27=\left( 27x\right)^{(3)/(4) }`

`\Longleftrightarrow \left( 27\right)^{(4)/(3) } =\left[ \left( 27x\right)^{(3)/(4) } \right]^{(4)/(3) }`

`\Longleftrightarrow \left( 27\right)^{(4)/(3) } =\left( 27x\right)^{(3)/(4) * (4)/(3) }`

`\Longleftrightarrow \left( 27\right)^{(4)/(3) } =27x`

`\Longleftrightarrow x=\frac{27^{(4)/(3) } }{27}`

`\Longleftrightarrow x=27^{(4)/(3) -1}`

`\Longleftrightarrow x=27^{(1)/(3) }`

`\Longleftrightarrow x=\sqrt[3]{27}`

`\Longleftrightarrow x=3`