Question
Simplify the expression
2548z−10z248z
Evaluate
5z(2z3)(−1)÷4−5(2z3)3÷4
Divide the numbers
5z(2z3)−0.25−5(2z3)3÷4
Convert the decimal into a fraction
More Steps

Evaluate
0.25
Convert the decimal into a fraction
10025
Reduce the fraction
41
5z(2z3)−41−5(2z3)3÷4
Divide the numbers
5z(2z3)−41−5(2z3)0.75
Convert the decimal into a fraction
More Steps

Evaluate
0.75
Convert the decimal into a fraction
10075
Reduce the fraction
43
5z(2z3)−41−5(2z3)43
Multiply the terms
More Steps

Multiply the terms
5z(2z3)−41
Reduce the numbers
More Steps

Calculate
5z×2411×z−43
Rewrite the expression
5z×241z431
Reduce the numbers
5z41×2411
5z41×2411
Multiply the numbers
2415×z41
Simplify
More Steps

Evaluate
2415
Rewrite the expression
425
Multiply by the Conjugate
42×4235423
Simplify
42×423548
Multiply the numbers
2548
2548z41
2548z41−5(2z3)43
Multiply the terms
2548z41−5×243z49
Calculate
2548z−5z248z
Reduce fractions to a common denominator
2548z−25z248z×2
Write all numerators above the common denominator
2548z−5z248z×2
Solution
2548z−10z248z
Show Solution

Find the roots
z=28128
Alternative Form
z≈0.917004
Evaluate
5z(2z3)(−1)÷4−5(2z3)3÷4
To find the roots of the expression,set the expression equal to 0
5z(2z3)(−1)÷4−5(2z3)3÷4=0
Find the domain
More Steps

Evaluate
⎩⎨⎧2z3>02z3=02z3≥0
Calculate
More Steps

Evaluate
2z3>0
Rewrite the expression
z3>0
The only way a base raised to an odd power can be greater than 0 is if the base is greater than 0
z>0
⎩⎨⎧z>02z3=02z3≥0
Calculate
More Steps

Evaluate
2z3=0
Rewrite the expression
z3=0
The only way a power can not be 0 is when the base not equals 0
z=0
⎩⎨⎧z>0z=02z3≥0
Calculate
More Steps

Evaluate
2z3≥0
Rewrite the expression
z3≥0
The only way a base raised to an odd power can be greater than or equal to 0 is if the base is greater than or equal to 0
z≥0
⎩⎨⎧z>0z=0z≥0
Find the intersection
z>0
5z(2z3)(−1)÷4−5(2z3)3÷4=0,z>0
Calculate
5z(2z3)(−1)÷4−5(2z3)3÷4=0
Divide the numbers
5z(2z3)−0.25−5(2z3)3÷4=0
Divide the numbers
5z(2z3)−0.25−5(2z3)0.75=0
Convert the decimal into a fraction
More Steps

Evaluate
0.25
Convert the decimal into a fraction
10025
Reduce the fraction
41
5z(2z3)−41−5(2z3)0.75=0
Convert the decimal into a fraction
More Steps

Evaluate
0.75
Convert the decimal into a fraction
10075
Reduce the fraction
43
5z(2z3)−41−5(2z3)43=0
Multiply the terms
More Steps

Multiply the terms
5z(2z3)−41
Reduce the numbers
More Steps

Calculate
5z×2411×z−43
Rewrite the expression
5z×241z431
Reduce the numbers
5z41×2411
5z41×2411
Multiply the numbers
2415×z41
Simplify
More Steps

Evaluate
2415
Rewrite the expression
425
Multiply by the Conjugate
42×4235423
Simplify
42×423548
Multiply the numbers
2548
2548z41
2548z41−5(2z3)43=0
Multiply the terms
2548z41−5423×z49=0
Evaluate the power
2548z41−548×z49=0
Factor the expression
z41(2548−548×z8)=0
Separate the equation into 2 possible cases
z41=02548−548×z8=0
Solve the equation
z=02548−548×z8=0
Solve the equation
More Steps

Evaluate
2548−548×z8=0
Move the constant to the right-hand side and change its sign
−548×z8=0−2548
Removing 0 doesn't change the value,so remove it from the expression
−548×z8=−2548
Change the signs on both sides of the equation
548×z8=2548
Multiply by the reciprocal
548×z8×5481=2548×5481
Multiply
z8=2548×5481
Multiply
More Steps

Evaluate
2548×5481
Reduce the numbers
248×481
Reduce the numbers
21×1
Multiply the numbers
21
z8=21
Take the root of both sides of the equation and remember to use both positive and negative roots
z=±821
Simplify the expression
More Steps

Evaluate
821
To take a root of a fraction,take the root of the numerator and denominator separately
8281
Simplify the radical expression
821
Multiply by the Conjugate
82×827827
Simplify
82×8278128
Multiply the numbers
28128
z=±28128
Separate the equation into 2 possible cases
z=28128z=−28128
z=0z=28128z=−28128
Check if the solution is in the defined range
z=0z=28128z=−28128,z>0
Solution
z=28128
Alternative Form
z≈0.917004
Show Solution
