20.5m3=4

To remove the radical on the left side of the equation, square both sides of the equation.

20.5m32=42

Rewrite 20.25m32 as ((20.25m)2)13.

(20.25m)23=42

Multiply the exponents in (20.25m)2.

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

Multiply the exponents in (20.16‾m)3.

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

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.

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