Question
Simplify the expression
2080−2er10
Evaluate
2080−2r5×r5e
Solution
More Steps

Evaluate
2r5×r5e
Multiply the terms with the same base by adding their exponents
2r5+5e
Add the numbers
2r10e
Multiply the numbers
2er10
2080−2er10
Show Solution

Factor the expression
2(1040−er10)
Evaluate
2080−2r5×r5e
Multiply
More Steps

Evaluate
2r5×r5e
Multiply the terms with the same base by adding their exponents
2r5+5e
Add the numbers
2r10e
Multiply the numbers
2er10
2080−2er10
Solution
2(1040−er10)
Show Solution

Find the roots
r1=−e101040e9,r2=e101040e9
Alternative Form
r1≈−1.812483,r2≈1.812483
Evaluate
2080−2r5×r5e
To find the roots of the expression,set the expression equal to 0
2080−2r5×r5e=0
Multiply
More Steps

Multiply the terms
2r5×r5e
Multiply the terms with the same base by adding their exponents
2r5+5e
Add the numbers
2r10e
Multiply the numbers
2er10
2080−2er10=0
Move the constant to the right-hand side and change its sign
−2er10=0−2080
Removing 0 doesn't change the value,so remove it from the expression
−2er10=−2080
Change the signs on both sides of the equation
2er10=2080
Divide both sides
2e2er10=2e2080
Divide the numbers
r10=2e2080
Cancel out the common factor 2
r10=e1040
Take the root of both sides of the equation and remember to use both positive and negative roots
r=±10e1040
Simplify the expression
More Steps

Evaluate
10e1040
To take a root of a fraction,take the root of the numerator and denominator separately
10e101040
Multiply by the Conjugate
10e×10e9101040×10e9
The product of roots with the same index is equal to the root of the product
10e×10e9101040e9
Multiply the numbers
More Steps

Evaluate
10e×10e9
The product of roots with the same index is equal to the root of the product
10e×e9
Calculate the product
10e10
Reduce the index of the radical and exponent with 10
e
e101040e9
r=±e101040e9
Separate the equation into 2 possible cases
r=e101040e9r=−e101040e9
Solution
r1=−e101040e9,r2=e101040e9
Alternative Form
r1≈−1.812483,r2≈1.812483
Show Solution
