Question
Simplify the expression
c2
Evaluate
(41a4c9)2(21a2c5)4
Evaluate the power
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Evaluate
(21a2c5)4
To raise a product to a power,raise each factor to that power
(21)4(a2)4(c5)4
Evaluate the power
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Evaluate
(21)4
To raise a fraction to a power,raise the numerator and denominator to that power
2414
Evaluate the power
241
Evaluate the power
161
161(a2)4(c5)4
Evaluate the power
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Evaluate
(a2)4
Multiply the exponents
a2×4
Multiply the terms
a8
161a8(c5)4
Evaluate the power
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Evaluate
(c5)4
Multiply the exponents
c5×4
Multiply the terms
c20
161a8c20
(41a4c9)2161a8c20
Evaluate the power
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Evaluate
(41a4c9)2
To raise a product to a power,raise each factor to that power
(41)2(a4)2(c9)2
Evaluate the power
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Evaluate
(41)2
To raise a fraction to a power,raise the numerator and denominator to that power
4212
Evaluate the power
421
Evaluate the power
161
161(a4)2(c9)2
Evaluate the power
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Evaluate
(a4)2
Multiply the exponents
a4×2
Multiply the terms
a8
161a8(c9)2
Evaluate the power
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Evaluate
(c9)2
Multiply the exponents
c9×2
Multiply the terms
c18
161a8c18
161a8c18161a8c20
Rewrite the expression
161a8c1816a8c20
Rewrite the expression
16a8c1816a8c20
Multiply by the reciprocal
16a8c20×a8c1816
Cancel out the common factor a8
16c20×c1816
Cancel out the common factor c18
16c2×16
Cancel out the common factor 16
c2×1
Solution
c2
Show Solution

Find the excluded values
a=0,c=0
Evaluate
(41a4c9)2(21a2c5)4
To find the excluded values,set the denominators equal to 0
(41a4c9)2=0
Evaluate the power
More Steps

Evaluate
(41a4c9)2
To raise a product to a power,raise each factor to that power
(41)2(a4)2(c9)2
Evaluate the power
More Steps

Evaluate
(41)2
To raise a fraction to a power,raise the numerator and denominator to that power
4212
Evaluate the power
421
Evaluate the power
161
161(a4)2(c9)2
Evaluate the power
More Steps

Evaluate
(a4)2
Multiply the exponents
a4×2
Multiply the terms
a8
161a8(c9)2
Evaluate the power
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Evaluate
(c9)2
Multiply the exponents
c9×2
Multiply the terms
c18
161a8c18
161a8c18=0
Evaluate
a8c18=0
Separate the equation into 2 possible cases
a8=0c18=0
The only way a power can be 0 is when the base equals 0
a=0c18=0
The only way a power can be 0 is when the base equals 0
a=0c=0
Solution
a=0,c=0
Show Solution
