Solve dd^5255-1 - ScanMath

Question

Simplify the expression

255 d^{6} - 1

Evaluate

d \times d^{5} \times 255 - 1

Solution

More Steps

Evaluate

d \times d^{5} \times 255

Multiply the terms with the same base by adding their exponents

d^{1 + 5} \times 255

Add the numbers

d^{6} \times 255

Use the commutative property to reorder the terms

255 d^{6}

255 d^{6} - 1

Show Solution

d_{1} = - \frac{6 25 5 ^{5}}{255}, d_{2} = \frac{6 25 5 ^{5}}{255}

Alternative Form

d_{1} \approx - 0.397109, d_{2} \approx 0.397109

Evaluate

d \times d^{5} \times 255 - 1

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

d \times d^{5} \times 255 - 1 = 0

Multiply

More Steps

Multiply the terms

d \times d^{5} \times 255

Multiply the terms with the same base by adding their exponents

d^{1 + 5} \times 255

Add the numbers

d^{6} \times 255

Use the commutative property to reorder the terms

255 d^{6}

255 d^{6} - 1 = 0

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

255 d^{6} = 0 + 1

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

255 d^{6} = 1

Divide both sides

\frac{255 d ^{6}}{255} = \frac{1}{255}

Divide the numbers

d^{6} = \frac{1}{255}

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

d = \pm 6 \frac{1}{255}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{255}

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

\frac{6 1}{6 255}

Simplify the radical expression

\frac{1}{6 255}

Multiply by the Conjugate

\frac{6 25 5 ^{5}}{6 255 \times 6 25 5 ^{5}}

Multiply the numbers

More Steps

Evaluate

6255 \times 6 25 5^{5}

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

6 255 \times 25 5^{5}

Calculate the product

6 25 5^{6}

Reduce the index of the radical and exponent with 6

255

\frac{6 25 5 ^{5}}{255}

d = \pm \frac{6 25 5 ^{5}}{255}

Separate the equation into 2 possible cases

d = \frac{6 25 5 ^{5}}{255} d = - \frac{6 25 5 ^{5}}{255}

Solution

d_{1} = - \frac{6 25 5 ^{5}}{255}, d_{2} = \frac{6 25 5 ^{5}}{255}

Alternative Form

d_{1} \approx - 0.397109, d_{2} \approx 0.397109

Show Solution