What is the answer to (2x^{3/2})^4=128 ?

The answer to (2x^{3/2})^4=128 is x=2^{1/2}

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(2x^{3/2})^4=128

(2 x^{\frac{3}{2}})^{4} = 128

x = 2^{\frac{1}{2}}

Decimal Notation

x = 1.41421 \dots

Solution steps

(2 x^{\frac{3}{2}})^{4} = 128

Move

128

to the left side

16 (x^{\frac{3}{2}})^{4} - 128 = 0

Factor

16 (x^{\frac{3}{2}})^{4} - 128 : 16 (x^{\frac{3}{2}} + 8^{\frac{1}{4}}) (x^{\frac{3}{2}} - 8^{\frac{1}{4}}) (x^{3} + 2 \cdot 2^{\frac{1}{2}})

16 (x^{\frac{3}{2}} + 8^{\frac{1}{4}}) (x^{\frac{3}{2}} - 8^{\frac{1}{4}}) (x^{3} + 2 \cdot 2^{\frac{1}{2}}) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x^{\frac{3}{2}} + 8^{\frac{1}{4}} = 0 or x^{\frac{3}{2}} - 8^{\frac{1}{4}} = 0 or x^{3} + 2 \cdot 2^{\frac{1}{2}} = 0

Solve

x^{\frac{3}{2}} + 8^{\frac{1}{4}} = 0 :

No Solution for

x \in R

Solve

x^{\frac{3}{2}} - 8^{\frac{1}{4}} = 0 : x = 2^{\frac{1}{2}}

Solve

x^{3} + 2 \cdot 2^{\frac{1}{2}} = 0 : x = - 2^{\frac{1}{2}}

x = 2^{\frac{1}{2}}, x = - 2^{\frac{1}{2}}

Verify Solutions:

x = 2^{\frac{1}{2}}

True

, x = - 2^{\frac{1}{2}}

False

The solution is

x = 2^{\frac{1}{2}}

8 = 2 x + 3

2 x + 1 = x + 1

4 + m - 2 = 4

What is the answer to (2x^{3/2})^4=128 ?
The answer to (2x^{3/2})^4=128 is x=2^{1/2}
Solve for x: (2x^{3/2})^4=128
The solution is x=2^{1/2}