# Solve for x 8x^(1/3)=x^(-2/3)

8×13=x-23
Rewrite the expression using the negative exponent rule b-n=1bn.
8×13=1×23
Subtract 1×23 from both sides of the equation.
8×13-1×23=0
Find the LCD of the terms in the equation.
Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.
1,x23,1
Since 1,x23,1 contain both numbers and variables, there are two steps to find the LCM. Find LCM for the numeric part 1,1,1 then find LCM for the variable part x23.
The LCM is the smallest positive number that all of the numbers divide into evenly.
1. List the prime factors of each number.
2. Multiply each factor the greatest number of times it occurs in either number.
The number 1 is not a prime number because it only has one positive factor, which is itself.
Not prime
The LCM of 1,1,1 is the result of multiplying all prime factors the greatest number of times they occur in either number.
1
The LCM of x23 is the result of multiplying all prime factors the greatest number of times they occur in either term.
x23
x23
Multiply each term by x23 and simplify.
Multiply each term in 8×13-1×23=0 by x23 in order to remove all the denominators from the equation.
8×13⋅x23-1×23⋅x23=0⋅x23
Simplify each term.
Multiply x13 by x23 by adding the exponents.
Move x23.
8(x23x13)-1×23⋅x23=0⋅x23
Use the power rule aman=am+n to combine exponents.
8×23+13-1×23⋅x23=0⋅x23
Combine the numerators over the common denominator.
8×2+13-1×23⋅x23=0⋅x23
Add 2 and 1.
8×33-1×23⋅x23=0⋅x23
Divide 3 by 3.
8×1-1×23⋅x23=0⋅x23
8×1-1×23⋅x23=0⋅x23
Simplify 8×1.
8x-1×23⋅x23=0⋅x23
Cancel the common factor of x23.
Move the leading negative in -1×23 into the numerator.
8x+-1×23⋅x23=0⋅x23
Cancel the common factor.
8x+-1×23⋅x23=0⋅x23
Rewrite the expression.
8x-1=0⋅x23
8x-1=0⋅x23
8x-1=0⋅x23
Multiply 0 by x23.
8x-1=0
8x-1=0
Solve the equation.
Add 1 to both sides of the equation.
8x=1
Divide each term by 8 and simplify.
Divide each term in 8x=1 by 8.
8×8=18
Cancel the common factor of 8.
Cancel the common factor.
8×8=18
Divide x by 1.
x=18
x=18
x=18
x=18
The result can be shown in multiple forms.
Exact Form:
x=18
Decimal Form:
x=0.125
Solve for x 8x^(1/3)=x^(-2/3)

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