Solve dd^5129-10 - ScanMath

Question

Simplify the expression

129 d^{6} - 10

Evaluate

d \times d^{5} \times 129 - 10

Solution

More Steps

Evaluate

d \times d^{5} \times 129

Multiply the terms with the same base by adding their exponents

d^{1 + 5} \times 129

Add the numbers

d^{6} \times 129

Use the commutative property to reorder the terms

129 d^{6}

129 d^{6} - 10

Show Solution

d_{1} = - \frac{6 10 \times 12 9 ^{5}}{129}, d_{2} = \frac{6 10 \times 12 9 ^{5}}{129}

Alternative Form

d_{1} \approx - 0.652983, d_{2} \approx 0.652983

Evaluate

d \times d^{5} \times 129 - 10

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

d \times d^{5} \times 129 - 10 = 0

Multiply

More Steps

Multiply the terms

d \times d^{5} \times 129

Multiply the terms with the same base by adding their exponents

d^{1 + 5} \times 129

Add the numbers

d^{6} \times 129

Use the commutative property to reorder the terms

129 d^{6}

129 d^{6} - 10 = 0

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

129 d^{6} = 0 + 10

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

129 d^{6} = 10

Divide both sides

\frac{129 d ^{6}}{129} = \frac{10}{129}

Divide the numbers

d^{6} = \frac{10}{129}

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

d = \pm 6 \frac{10}{129}

Simplify the expression

More Steps

Evaluate

6 \frac{10}{129}

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

\frac{6 10}{6 129}

Multiply by the Conjugate

\frac{6 10 \times 6 12 9 ^{5}}{6 129 \times 6 12 9 ^{5}}

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

\frac{6 10 \times 12 9 ^{5}}{6 129 \times 6 12 9 ^{5}}

Multiply the numbers

More Steps

Evaluate

6129 \times 6 12 9^{5}

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

6 129 \times 12 9^{5}

Calculate the product

6 12 9^{6}

Reduce the index of the radical and exponent with 6

129

\frac{6 10 \times 12 9 ^{5}}{129}

d = \pm \frac{6 10 \times 12 9 ^{5}}{129}

Separate the equation into 2 possible cases

d = \frac{6 10 \times 12 9 ^{5}}{129} d = - \frac{6 10 \times 12 9 ^{5}}{129}

Solution

d_{1} = - \frac{6 10 \times 12 9 ^{5}}{129}, d_{2} = \frac{6 10 \times 12 9 ^{5}}{129}

Alternative Form

d_{1} \approx - 0.652983, d_{2} \approx 0.652983

Show Solution