Solve 1v^4207-157 - Socratic AI (ScanMath)

Question

Simplify the expression

207 v^{4} - 157

Evaluate

1 \times v^{4} \times 207 - 157

Solution

More Steps

Evaluate

1 \times v^{4} \times 207

Rewrite the expression

v^{4} \times 207

Use the commutative property to reorder the terms

207 v^{4}

207 v^{4} - 157

Show Solution

v_{1} = - \frac{4 157 \times 20 7 ^{3}}{207}, v_{2} = \frac{4 157 \times 20 7 ^{3}}{207}

Alternative Form

v_{1} \approx - 0.933216, v_{2} \approx 0.933216

Evaluate

1 \times v^{4} \times 207 - 157

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

1 \times v^{4} \times 207 - 157 = 0

Multiply the terms

More Steps

Multiply the terms

1 \times v^{4} \times 207

Rewrite the expression

v^{4} \times 207

Use the commutative property to reorder the terms

207 v^{4}

207 v^{4} - 157 = 0

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

207 v^{4} = 0 + 157

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

207 v^{4} = 157

Divide both sides

\frac{207 v ^{4}}{207} = \frac{157}{207}

Divide the numbers

v^{4} = \frac{157}{207}

Take the root of both sides of the equation and remember to use both positive and negative roots

v = \pm 4 \frac{157}{207}

Simplify the expression

More Steps

Evaluate

4 \frac{157}{207}

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

\frac{4 157}{4 207}

Multiply by the Conjugate

\frac{4 157 \times 4 20 7 ^{3}}{4 207 \times 4 20 7 ^{3}}

The product of roots with the same index is equal to the root of the product

\frac{4 157 \times 20 7 ^{3}}{4 207 \times 4 20 7 ^{3}}

Multiply the numbers

More Steps

Evaluate

4207 \times 4 20 7^{3}

The product of roots with the same index is equal to the root of the product

4 207 \times 20 7^{3}

Calculate the product

4 20 7^{4}

Reduce the index of the radical and exponent with 4

207

\frac{4 157 \times 20 7 ^{3}}{207}

v = \pm \frac{4 157 \times 20 7 ^{3}}{207}

Separate the equation into 2 possible cases

v = \frac{4 157 \times 20 7 ^{3}}{207} v = - \frac{4 157 \times 20 7 ^{3}}{207}

Solution

v_{1} = - \frac{4 157 \times 20 7 ^{3}}{207}, v_{2} = \frac{4 157 \times 20 7 ^{3}}{207}

Alternative Form

v_{1} \approx - 0.933216, v_{2} \approx 0.933216

Show Solution