Question
Simplify the expression
99t2r2q2s2−4
Evaluate
((((1÷2)sqrt×2)2((1÷2)sqrt×3)2)−((1÷3)sqrt×3)2)÷((1÷2)sqrt×3(1÷2)sqrt×3)
Divide the numbers
(((0.5sqrt×2)2((1÷2)sqrt×3)2)−((1÷3)sqrt×3)2)÷((1÷2)sqrt×3(1÷2)sqrt×3)
Multiply the terms
(((sqrt)2((1÷2)sqrt×3)2)−((1÷3)sqrt×3)2)÷((1÷2)sqrt×3(1÷2)sqrt×3)
Divide the numbers
(((sqrt)2(0.5sqrt×3)2)−((1÷3)sqrt×3)2)÷((1÷2)sqrt×3(1÷2)sqrt×3)
Multiply the terms
(((sqrt)2(1.5sqrt)2)−((1÷3)sqrt×3)2)÷((1÷2)sqrt×3(1÷2)sqrt×3)
Convert the decimal into a fraction
More Steps

Evaluate
1.5
Convert the decimal into a fraction
1015
Reduce the fraction
23
(((sqrt)2(23sqrt)2)−((1÷3)sqrt×3)2)÷((1÷2)sqrt×3(1÷2)sqrt×3)
Multiply the terms
More Steps

Evaluate
(sqrt)2(23sqrt)2
Rewrite the expression
s2q2r2t2×49s2q2r2t2
Use the commutative property to reorder the terms
49s2q2r2t2s2q2r2t2
Multiply the terms
More Steps

Evaluate
s2×s2
Use the product rule an×am=an+m to simplify the expression
s2+2
Add the numbers
s4
49s4q2r2t2q2r2t2
Multiply the terms
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Evaluate
q2×q2
Use the product rule an×am=an+m to simplify the expression
q2+2
Add the numbers
q4
49s4q4r2t2r2t2
Multiply the terms
More Steps

Evaluate
r2×r2
Use the product rule an×am=an+m to simplify the expression
r2+2
Add the numbers
r4
49s4q4r4t2×t2
Multiply the terms
More Steps

Evaluate
t2×t2
Use the product rule an×am=an+m to simplify the expression
t2+2
Add the numbers
t4
49s4q4r4t4
(49s4q4r4t4−((1÷3)sqrt×3)2)÷((1÷2)sqrt×3(1÷2)sqrt×3)
Rewrite the expression
(49s4q4r4t4−(31sqrt×3)2)÷((1÷2)sqrt×3(1÷2)sqrt×3)
Multiply the terms
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Multiply the terms
31sqrt×3
Multiply the terms
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Evaluate
31×3
Reduce the fraction
1×1
Any expression multiplied by 1 remains the same
1
sqrt
(49s4q4r4t4−(sqrt)2)÷((1÷2)sqrt×3(1÷2)sqrt×3)
Rewrite the expression
(49s4q4r4t4−s2q2r2t2)÷((1÷2)sqrt×3(1÷2)sqrt×3)
Divide the numbers
(49s4q4r4t4−s2q2r2t2)÷(0.5sqrt×3(1÷2)sqrt×3)
Divide the numbers
(49s4q4r4t4−s2q2r2t2)÷(0.5sqrt×3×0.5sqrt×3)
Multiply
More Steps

Multiply the terms
0.5sqrt×3×0.5sqrt×3
Multiply the terms
More Steps

Evaluate
0.5×3×0.5×3
Multiply the terms
1.5×0.5×3
Multiply the terms
0.75×3
Multiply the numbers
2.25
2.25sqrtsqrt
Multiply the terms
2.25s2qrtqrt
Multiply the terms
2.25s2q2rtrt
Multiply the terms
2.25s2q2r2t×t
Multiply the terms
2.25s2q2r2t2
(49s4q4r4t4−s2q2r2t2)÷2.25s2q2r2t2
Solution
More Steps

Evaluate
2.25
Convert the decimal into a fraction
100225
Reduce the fraction
49
Rewrite the expression
(49s4q4r4t4−s2q2r2t2)÷49s2q2r2t2
Multiply by the reciprocal
(49s4q4r4t4−s2q2r2t2)×9s2q2r2t24
Rewrite the expression
More Steps

Evaluate
49s4q4r4t4−s2q2r2t2
Rewrite the expression
49s4q4r4t4−s2q2r2t2
Reduce fractions to a common denominator
49s4q4r4t4−4s2q2r2t2×4
Write all numerators above the common denominator
49s4q4r4t4−s2q2r2t2×4
Use the commutative property to reorder the terms
49s4q4r4t4−4s2q2r2t2
49s4q4r4t4−4s2q2r2t2×9s2q2r2t24
Rewrite the expression
4s2(9q4r4t4s2−4q2r2t2)×9s2q2r2t24
Cancel out the common factor s2
49q4r4t4s2−4q2r2t2×9q2r2t24
Rewrite the expression
4q2(9r4t4q2s2−4r2t2)×9q2r2t24
Cancel out the common factor q2
49r4t4q2s2−4r2t2×9r2t24
Rewrite the expression
4r2(9t4r2q2s2−4t2)×9r2t24
Cancel out the common factor r2
49t4r2q2s2−4t2×9t24
Rewrite the expression
4t2(9t2r2q2s2−4)×9t24
Cancel out the common factor t2
49t2r2q2s2−4×94
Cancel out the common factor 4
(9t2r2q2s2−4)×91
Multiply the terms
99t2r2q2s2−4
99t2r2q2s2−4
Show Solution

Find the excluded values
s=0,q=0,r=0,t=0
Evaluate
(((((1÷2)sqrt×2)2)(((1÷2)sqrt×3)2))−(((1÷3)sqrt×3)2))÷((1÷2)sqrt×3(1÷2)sqrt×3)
To find the excluded values,set the denominators equal to 0
(1÷2)sqrt×3(1÷2)sqrt×3=0
Simplify
More Steps

Evaluate
(1÷2)sqrt×3(1÷2)sqrt×3
Divide the numbers
0.5sqrt×3(1÷2)sqrt×3
Divide the numbers
0.5sqrt×3×0.5sqrt×3
Multiply the terms
More Steps

Evaluate
0.5×3×0.5×3
Multiply the terms
1.5×0.5×3
Multiply the terms
0.75×3
Multiply the numbers
2.25
2.25sqrtsqrt
Multiply the terms
2.25s2qrtqrt
Multiply the terms
2.25s2q2rtrt
Multiply the terms
2.25s2q2r2t×t
Multiply the terms
2.25s2q2r2t2
2.25s2q2r2t2=0
Evaluate
s2q2r2t2=0
Separate the equation into 4 possible cases
s2=0q2=0r2=0t2=0
The only way a power can be 0 is when the base equals 0
s=0q2=0r2=0t2=0
The only way a power can be 0 is when the base equals 0
s=0q=0r2=0t2=0
The only way a power can be 0 is when the base equals 0
s=0q=0r=0t2=0
The only way a power can be 0 is when the base equals 0
s=0q=0r=0t=0
Solution
s=0,q=0,r=0,t=0
Show Solution
