Solve d^663-1 - ScanMath

Question

Simplify the expression

63 d^{6} - 1

Evaluate

d^{6} \times 63 - 1

Solution

63 d^{6} - 1

Show Solution

d_{1} = - \frac{6 6 3 ^{5}}{63}, d_{2} = \frac{6 6 3 ^{5}}{63}

Alternative Form

d_{1} \approx - 0.501314, d_{2} \approx 0.501314

Evaluate

d^{6} \times 63 - 1

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

d^{6} \times 63 - 1 = 0

Use the commutative property to reorder the terms

63 d^{6} - 1 = 0

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

63 d^{6} = 0 + 1

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

63 d^{6} = 1

Divide both sides

\frac{63 d ^{6}}{63} = \frac{1}{63}

Divide the numbers

d^{6} = \frac{1}{63}

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

d = \pm 6 \frac{1}{63}

Simplify the expression

More Steps

Evaluate

6 \frac{1}{63}

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

\frac{6 1}{6 63}

Simplify the radical expression

\frac{1}{6 63}

Multiply by the Conjugate

\frac{6 6 3 ^{5}}{6 63 \times 6 6 3 ^{5}}

Multiply the numbers

More Steps

Evaluate

663 \times 6 6 3^{5}

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

6 63 \times 6 3^{5}

Calculate the product

6 6 3^{6}

Reduce the index of the radical and exponent with 6

63

\frac{6 6 3 ^{5}}{63}

d = \pm \frac{6 6 3 ^{5}}{63}

Separate the equation into 2 possible cases

d = \frac{6 6 3 ^{5}}{63} d = - \frac{6 6 3 ^{5}}{63}

Solution

d_{1} = - \frac{6 6 3 ^{5}}{63}, d_{2} = \frac{6 6 3 ^{5}}{63}

Alternative Form

d_{1} \approx - 0.501314, d_{2} \approx 0.501314

Show Solution