Solve v^327-1 - ScanMath

Question

Simplify the expression

27 v^{3} - 1

Evaluate

v^{3} \times 27 - 1

Solution

27 v^{3} - 1

Show Solution

(3 v - 1) (9 v^{2} + 3 v + 1)

Evaluate

v^{3} \times 27 - 1

Use the commutative property to reorder the terms

27 v^{3} - 1

Rewrite the expression in exponential form

(3 v)^{3} - 1^{3}

Use a^{3} - b^{3} = (a - b) (a^{2} + ab + b^{2}) to factor the expression

(3 v - 1) ((3 v)^{2} + 3 v \times 1 + 1^{2})

Evaluate

More Steps

Evaluate

(3 v)^{2}

To raise a product to a power,raise each factor to that power

3^{2} v^{2}

Evaluate the power

9 v^{2}

(3 v - 1) (9 v^{2} + 3 v \times 1 + 1^{2})

Any expression multiplied by 1 remains the same

(3 v - 1) (9 v^{2} + 3 v + 1^{2})

Solution

(3 v - 1) (9 v^{2} + 3 v + 1)

Show Solution

v = \frac{1}{3}

Alternative Form

v = 0. \dot{3}

Evaluate

v^{3} \times 27 - 1

To find the roots of the expression,set the expression equal to 0

v^{3} \times 27 - 1 = 0

Use the commutative property to reorder the terms

27 v^{3} - 1 = 0

Move the constant to the right-hand side and change its sign

27 v^{3} = 0 + 1

Removing 0 doesn't change the value,so remove it from the expression

27 v^{3} = 1

Divide both sides

\frac{27 v ^{3}}{27} = \frac{1}{27}

Divide the numbers

v^{3} = \frac{1}{27}

Take the 3 -th root on both sides of the equation

3 v^{3} = 3 \frac{1}{27}

Calculate

v = 3 \frac{1}{27}

Solution

More Steps

Evaluate

3 \frac{1}{27}

To take a root of a fraction,take the root of the numerator and denominator separately

\frac{3 1}{3 27}

Simplify the radical expression

\frac{1}{3 27}

Simplify the radical expression

More Steps

Evaluate

327

Write the number in exponential form with the base of 3

3 3^{3}

Reduce the index of the radical and exponent with 3

3

\frac{1}{3}

v = \frac{1}{3}

Alternative Form

v = 0. \dot{3}

Show Solution