Solve m^48378-1 - ScanMath

Question

Simplify the expression

8378 m^{4} - 1

Evaluate

m^{4} \times 8378 - 1

Solution

8378 m^{4} - 1

Show Solution

m_{1} = - \frac{4 837 8 ^{3}}{8378}, m_{2} = \frac{4 837 8 ^{3}}{8378}

Alternative Form

m_{1} \approx - 0.104524, m_{2} \approx 0.104524

Evaluate

m^{4} \times 8378 - 1

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

m^{4} \times 8378 - 1 = 0

Use the commutative property to reorder the terms

8378 m^{4} - 1 = 0

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

8378 m^{4} = 0 + 1

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

8378 m^{4} = 1

Divide both sides

\frac{8378 m ^{4}}{8378} = \frac{1}{8378}

Divide the numbers

m^{4} = \frac{1}{8378}

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

m = \pm 4 \frac{1}{8378}

Simplify the expression

More Steps

Evaluate

4 \frac{1}{8378}

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

\frac{4 1}{4 8378}

Simplify the radical expression

\frac{1}{4 8378}

Multiply by the Conjugate

\frac{4 837 8 ^{3}}{4 8378 \times 4 837 8 ^{3}}

Multiply the numbers

More Steps

Evaluate

48378 \times 4 837 8^{3}

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

4 8378 \times 837 8^{3}

Calculate the product

4 837 8^{4}

Reduce the index of the radical and exponent with 4

8378

\frac{4 837 8 ^{3}}{8378}

m = \pm \frac{4 837 8 ^{3}}{8378}

Separate the equation into 2 possible cases

m = \frac{4 837 8 ^{3}}{8378} m = - \frac{4 837 8 ^{3}}{8378}

Solution

m_{1} = - \frac{4 837 8 ^{3}}{8378}, m_{2} = \frac{4 837 8 ^{3}}{8378}

Alternative Form

m_{1} \approx - 0.104524, m_{2} \approx 0.104524

Show Solution