Solve 3954-5a^5a - ScanMath

Question

Simplify the expression

3954 - 5 a^{6}

Evaluate

3954 - 5 a^{5} \times a

Solution

More Steps

Evaluate

5 a^{5} \times a

Multiply the terms with the same base by adding their exponents

5 a^{5 + 1}

Add the numbers

5 a^{6}

3954 - 5 a^{6}

Show Solution

a_{1} = - \frac{6 12356250}{5}, a_{2} = \frac{6 12356250}{5}

Alternative Form

a_{1} \approx - 3.040963, a_{2} \approx 3.040963

Evaluate

3954 - 5 a^{5} \times a

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

3954 - 5 a^{5} \times a = 0

Multiply

More Steps

Multiply the terms

5 a^{5} \times a

Multiply the terms with the same base by adding their exponents

5 a^{5 + 1}

Add the numbers

5 a^{6}

3954 - 5 a^{6} = 0

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

- 5 a^{6} = 0 - 3954

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

- 5 a^{6} = - 3954

Change the signs on both sides of the equation

5 a^{6} = 3954

Divide both sides

\frac{5 a ^{6}}{5} = \frac{3954}{5}

Divide the numbers

a^{6} = \frac{3954}{5}

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

a = \pm 6 \frac{3954}{5}

Simplify the expression

More Steps

Evaluate

6 \frac{3954}{5}

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

\frac{6 3954}{6 5}

Multiply by the Conjugate

\frac{6 3954 \times 6 5 ^{5}}{6 5 \times 6 5 ^{5}}

Simplify

\frac{6 3954 \times 6 3125}{6 5 \times 6 5 ^{5}}

Multiply the numbers

More Steps

Evaluate

63954 \times 63125

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

6 3954 \times 3125

Calculate the product

612356250

\frac{6 12356250}{6 5 \times 6 5 ^{5}}

Multiply the numbers

More Steps

Evaluate

65 \times 6 5^{5}

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

6 5 \times 5^{5}

Calculate the product

6 5^{6}

Reduce the index of the radical and exponent with 6

5

\frac{6 12356250}{5}

a = \pm \frac{6 12356250}{5}

Separate the equation into 2 possible cases

a = \frac{6 12356250}{5} a = - \frac{6 12356250}{5}

Solution

a_{1} = - \frac{6 12356250}{5}, a_{2} = \frac{6 12356250}{5}

Alternative Form

a_{1} \approx - 3.040963, a_{2} \approx 3.040963

Show Solution