gudetamatama101
Answered

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RATIONAL EXPONENTS pls help what do i do??

RATIONAL EXPONENTS Pls Help What Do I Do class=

Sagot :

Hrishii

Answer:

x = 3

Step-by-step explanation:

  • [tex]26=-1+(27x)^{\frac{3}{4}}[/tex]

  • [tex]\implies 26+1=27^{\frac{3}{4}} x^{\frac{3}{4}}[/tex]

  • [tex]\implies 27\div 27^{\frac{3}{4}} =x^{\frac{3}{4}}[/tex]

  • [tex]\implies 27^{1-\frac{3}{4}} =x^{\frac{3}{4}}[/tex]

  • [tex]\implies 27^{\frac{4-3}{4}} =x^{\frac{3}{4}}[/tex]

  • [tex]\implies 27^{\frac{1}{\cancel 4}} =x^{\frac{3}{\cancel 4}}[/tex]

  • [tex]\implies 27 =x^{3}[/tex]

  • [tex]\implies 27^{\frac{1}{3}} =x[/tex]

  • [tex]\implies (3^3)^{\frac{1}{3}} =x[/tex]

  • [tex]\implies x = 3[/tex]

Answer:

x = 3

Step-by-step explanation:

[tex]26=-1+\left( 27x\right)^{\frac{3}{4} }[/tex]

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

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

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

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

[tex]\Longleftrightarrow x=\frac{27^{\frac{4}{3} } }{27}[/tex]

[tex]\Longleftrightarrow x=27^{\frac{4}{3} -1}[/tex]

[tex]\Longleftrightarrow x=27^{\frac{1}{3} }[/tex]

[tex]\Longleftrightarrow x=\sqrt[3]{27}[/tex]

[tex]\Longleftrightarrow x=3[/tex]

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