Question
Simplify the expression
1458x4−27
Evaluate
18x3×81x−27
Solution
More Steps

Evaluate
18x3×81x
Multiply the terms
1458x3×x
Multiply the terms with the same base by adding their exponents
1458x3+1
Add the numbers
1458x4
1458x4−27
Show Solution

Factor the expression
27(54x4−1)
Evaluate
18x3×81x−27
Multiply
More Steps

Evaluate
18x3×81x
Multiply the terms
1458x3×x
Multiply the terms with the same base by adding their exponents
1458x3+1
Add the numbers
1458x4
1458x4−27
Solution
27(54x4−1)
Show Solution

Find the roots
x1=−544543,x2=544543
Alternative Form
x1≈−0.368894,x2≈0.368894
Evaluate
18x3×81x−27
To find the roots of the expression,set the expression equal to 0
18x3×81x−27=0
Multiply
More Steps

Multiply the terms
18x3×81x
Multiply the terms
1458x3×x
Multiply the terms with the same base by adding their exponents
1458x3+1
Add the numbers
1458x4
1458x4−27=0
Move the constant to the right-hand side and change its sign
1458x4=0+27
Removing 0 doesn't change the value,so remove it from the expression
1458x4=27
Divide both sides
14581458x4=145827
Divide the numbers
x4=145827
Cancel out the common factor 27
x4=541
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±4541
Simplify the expression
More Steps

Evaluate
4541
To take a root of a fraction,take the root of the numerator and denominator separately
45441
Simplify the radical expression
4541
Multiply by the Conjugate
454×45434543
Multiply the numbers
More Steps

Evaluate
454×4543
The product of roots with the same index is equal to the root of the product
454×543
Calculate the product
4544
Reduce the index of the radical and exponent with 4
54
544543
x=±544543
Separate the equation into 2 possible cases
x=544543x=−544543
Solution
x1=−544543,x2=544543
Alternative Form
x1≈−0.368894,x2≈0.368894
Show Solution
