Solve for m cube root of square root of 2^(0.5m)=4

Math
20.5m3=4
To remove the radical on the left side of the equation, square both sides of the equation.
20.5m32=42
Simplify each side of the equation.
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Rewrite 20.25m32 as ((20.25m)2)13.
(20.25m)23=42
Multiply the exponents in (20.25m)2.
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Apply the power rule and multiply exponents, (am)n=amn.
20.25m⋅23=42
Multiply 2 by 0.25.
20.5m3=42
20.5m3=42
Raise 4 to the power of 2.
20.5m3=16
20.5m3=16
To remove the radical on the left side of the equation, cube both sides of the equation.
20.5m33=163
Simplify each side of the equation.
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Multiply the exponents in (20.16‾m)3.
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Apply the power rule and multiply exponents, (am)n=amn.
20.16‾m⋅3=163
Multiply 3 by 0.16‾.
20.5m=163
20.5m=163
Raise 16 to the power of 3.
20.5m=4096
20.5m=4096
Solve for m.
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Create equivalent expressions in the equation that all have equal bases.
20.5m=212
Since the bases are the same, then two expressions are only equal if the exponents are also equal.
0.5m=12
Divide each term by 0.5 and simplify.
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Divide each term in 0.5m=12 by 0.5.
0.5m0.5=120.5
Cancel the common factor of 0.5.
m=120.5
Divide 12 by 0.5.
m=24
m=24
m=24
Solve for m cube root of square root of 2^(0.5m)=4

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