# Solve for z 3z^5-5=12

3z5-5=12
Move all terms not containing z to the right side of the equation.
Add 5 to both sides of the equation.
3z5=12+5
3z5=17
3z5=17
Divide each term by 3 and simplify.
Divide each term in 3z5=17 by 3.
3z53=173
Cancel the common factor of 3.
Cancel the common factor.
3z53=173
Divide z5 by 1.
z5=173
z5=173
z5=173
Take the 5th root of both sides of the equation to eliminate the exponent on the left side.
z=1735
Simplify 1735.
Rewrite 1735 as 17535.
z=17535
Multiply 17535 by 354354.
z=17535⋅354354
Combine and simplify the denominator.
Multiply 17535 and 354354.
z=17535435354
Raise 35 to the power of 1.
z=175354351354
Use the power rule aman=am+n to combine exponents.
z=175354351+4
z=175354355
Rewrite 355 as 3.
Use axn=axn to rewrite 35 as 315.
z=175354(315)5
Apply the power rule and multiply exponents, (am)n=amn.
z=175354315⋅5
Combine 15 and 5.
z=175354355
Cancel the common factor of 5.
Cancel the common factor.
z=175354355
Divide 1 by 1.
z=17535431
z=17535431
Evaluate the exponent.
z=1753543
z=1753543
z=1753543
Simplify the numerator.
Rewrite 354 as (34)15.
z=1753453
Raise 3 to the power of 4.
z=1758153
z=1758153
Simplify the numerator.
Combine using the product rule for radicals.
z=17⋅8153
Multiply 17 by 81.
z=137753
z=137753
z=137753
The result can be shown in multiple forms.
Exact Form:
z=137753
Decimal Form:
z=1.41470384…
Solve for z 3z^5-5=12

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