6.5B Solving Rational Exponent Equations

Solve the equation. Check for extraneous solutions.
1.  $\left(2x+1\right)^{\frac{1}{3}}=-3$  

• -1

• -14

• 13

• 0

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.A.2

Solve the equation. Check for extraneous solutions.
2.  $\left(x+12\right)^{\frac{2}{5}}=4$  

• -44 and 20

• -44

• 20

• -2

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.A.2

Solve the equation. Check for extraneous solutions.
3.  $2x^{\frac{3}{4}}=16$  

•  $\pm16$  
  

• -16

• No Solution

• 16

Tags

CCSS.HSA.REI.A.2

CCSS.HSN.RN.A.1

Solve the equation. Check for extraneous solutions.
4.  $\left(7x-3\right)^{\frac{1}{2}}=5$  

•  $\pm4$  
  

• 4

• No Solution

•  $\frac{13}{7}$  
  

Tags

CCSS.HSA.REI.A.2

Solve the equation. Check for extraneous solutions.
5.  $4x^{\frac{1}{2}}-5=27$  

•  $\frac{367}{2}$  
  

• 121

• 64

• 256

Tags

CCSS.HSA.REI.A.2

Solve the equation. Check for extraneous solutions.
6.  $\left(x+3\right)^{\frac{6}{5}}-2=62$  

• 29

• -35

• No Solution

• 29 and -35

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSA.REI.A.2

Solve the equation. Check for extraneous solutions.
7.  $\left(2x+1\right)^{\frac{1}{3}}=1$  

• 0

• 1

• 0 and 1

• No Solution

Tags

CCSS.HSA.REI.A.2

Solve the equation. Check for extraneous solutions.
8.  $\left(x-2\right)^{\frac{2}{3}}-4=5$  

• -25

• 29

• -25 and 29

• No Solution

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.A.2

Solve the equation. Check for extraneous solutions.
9.  $3x^{\frac{4}{3}}+5=53$  

• 8

• -8

•  $\pm8$  
  

• No Solution

Tags

CCSS.HSA.REI.A.1

CCSS.HSA.REI.A.2

Solve the equation. Check for extraneous solutions.
10.  $\left(x+7\right)^{\frac{1}{2}}=x-5$  

• 9

• 2

• 9 and 2 
  

• No Solution

Tags

CCSS.HSA.REI.A.2