Question
Simplify the expression
z7−5z6
Evaluate
(z−5)z3×z3
Multiply the terms with the same base by adding their exponents
(z−5)z3+3
Add the numbers
(z−5)z6
Multiply the terms
z6(z−5)
Apply the distributive property
z6×z−z6×5
Multiply the terms
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Evaluate
z6×z
Use the product rule an×am=an+m to simplify the expression
z6+1
Add the numbers
z7
z7−z6×5
Solution
z7−5z6
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Find the roots
z1=0,z2=5
Evaluate
(z−5)(z3)(z3)
To find the roots of the expression,set the expression equal to 0
(z−5)(z3)(z3)=0
Calculate
(z−5)z3(z3)=0
Calculate
(z−5)z3×z3=0
Multiply the terms
More Steps
Multiply the terms
(z−5)z3×z3
Multiply the terms with the same base by adding their exponents
(z−5)z3+3
Add the numbers
(z−5)z6
Multiply the terms
z6(z−5)
z6(z−5)=0
Separate the equation into 2 possible cases
z6=0z−5=0
The only way a power can be 0 is when the base equals 0
z=0z−5=0
Solve the equation
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Evaluate
z−5=0
Move the constant to the right-hand side and change its sign
z=0+5
Removing 0 doesn't change the value,so remove it from the expression
z=5
z=0z=5
Solution
z1=0,z2=5
Show Solution