3z5-5=12

Add 5 to both sides of the equation.

3z5=12+5

Add 12 and 5.

3z5=17

3z5=17

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

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

Add 1 and 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