Solve dd^3151-2 - ScanMath

Question

Simplify the expression

151 d^{4} - 2

Evaluate

d \times d^{3} \times 151 - 2

Solution

More Steps

Evaluate

d \times d^{3} \times 151

Multiply the terms with the same base by adding their exponents

d^{1 + 3} \times 151

Add the numbers

d^{4} \times 151

Use the commutative property to reorder the terms

151 d^{4}

151 d^{4} - 2

Show Solution

d_{1} = - \frac{4 2 \times 15 1 ^{3}}{151}, d_{2} = \frac{4 2 \times 15 1 ^{3}}{151}

Alternative Form

d_{1} \approx - 0.339245, d_{2} \approx 0.339245

Evaluate

d \times d^{3} \times 151 - 2

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

d \times d^{3} \times 151 - 2 = 0

Multiply

More Steps

Multiply the terms

d \times d^{3} \times 151

Multiply the terms with the same base by adding their exponents

d^{1 + 3} \times 151

Add the numbers

d^{4} \times 151

Use the commutative property to reorder the terms

151 d^{4}

151 d^{4} - 2 = 0

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

151 d^{4} = 0 + 2

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

151 d^{4} = 2

Divide both sides

\frac{151 d ^{4}}{151} = \frac{2}{151}

Divide the numbers

d^{4} = \frac{2}{151}

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

d = \pm 4 \frac{2}{151}

Simplify the expression

More Steps

Evaluate

4 \frac{2}{151}

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

\frac{4 2}{4 151}

Multiply by the Conjugate

\frac{4 2 \times 4 15 1 ^{3}}{4 151 \times 4 15 1 ^{3}}

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

\frac{4 2 \times 15 1 ^{3}}{4 151 \times 4 15 1 ^{3}}

Multiply the numbers

More Steps

Evaluate

4151 \times 4 15 1^{3}

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

4 151 \times 15 1^{3}

Calculate the product

4 15 1^{4}

Reduce the index of the radical and exponent with 4

151

\frac{4 2 \times 15 1 ^{3}}{151}

d = \pm \frac{4 2 \times 15 1 ^{3}}{151}

Separate the equation into 2 possible cases

d = \frac{4 2 \times 15 1 ^{3}}{151} d = - \frac{4 2 \times 15 1 ^{3}}{151}

Solution

d_{1} = - \frac{4 2 \times 15 1 ^{3}}{151}, d_{2} = \frac{4 2 \times 15 1 ^{3}}{151}

Alternative Form

d_{1} \approx - 0.339245, d_{2} \approx 0.339245

Show Solution