Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
c21
Evaluate
(1÷2a2c5)4÷(1÷4a4c9)2
Rewrite the expression
(2a2c51)4÷(1÷4a4c9)2
Rewrite the expression
(2a2c51)4÷(4a4c91)2
Evaluate the power
(2a2c5)−4÷(4a4c91)2
Evaluate the power
(2a2c5)−4÷(4a4c9)−2
Express with a positive exponent using a−n=an1
(2a2c5)41÷(4a4c9)−2
Express with a positive exponent using a−n=an1
(2a2c5)41÷(4a4c9)21
Multiply by the reciprocal
(2a2c5)41×(4a4c9)2
Rewrite the expression
(2a2c5)41×16a8c18
Rewrite the expression
16a8c201×16a8c18
Cancel out the common factor 16
a8c201×a8c18
Cancel out the common factor a8
c201×c18
Cancel out the common factor c18
c21×1
Solution
c21
Show Solution
Find the excluded values
a=0,c=0
Evaluate
(1÷2a2c5)4÷(1÷4a4c9)2
To find the excluded values,set the denominators equal to 0
a2c5=0a4c9=0(1÷4a4c9)2=0
Solve the equations
More Steps
Evaluate
a2c5=0
Separate the equation into 2 possible cases
a2=0c5=0
The only way a power can be 0 is when the base equals 0
a=0c5=0
The only way a power can be 0 is when the base equals 0
a=0c=0
a=0c=0a4c9=0(1÷4a4c9)2=0
Solve the equations
More Steps
Evaluate
a4c9=0
Separate the equation into 2 possible cases
a4=0c9=0
The only way a power can be 0 is when the base equals 0
a=0c9=0
The only way a power can be 0 is when the base equals 0
a=0c=0
a=0c=0a=0c=0(1÷4a4c9)2=0
Solve the equations
More Steps
Evaluate
(1÷4a4c9)2=0
Simplify
More Steps
Evaluate
(1÷4a4c9)2
Rewrite the expression
(4a4c91)2
Evaluate the power
(4a4c9)−2
To raise a product to a power,raise each factor to that power
4−2(a4)−2(c9)−2
Evaluate the power
161(a4)−2(c9)−2
Evaluate the power
161a−8(c9)−2
Evaluate the power
161a−8c−18
161a−8c−18=0
Rewrite the expression
16a8c181=0
Cross multiply
1=16a8c18×0
Simplify the equation
1=0
Check the equality
false
a=0c=0a=0c=0false
Solution
a=0,c=0
Show Solution