Solve 7a(a^4)-(a^4)

Question

Simplify the expression

7 a^{5} - a^{4}

Evaluate

7 a \times a^{4} - a^{4}

Solution

More Steps

Evaluate

7 a \times a^{4}

Multiply the terms with the same base by adding their exponents

7 a^{1 + 4}

Add the numbers

7 a^{5}

7 a^{5} - a^{4}

Show Solution

a^{4} (7 a - 1)

Evaluate

7 a \times a^{4} - a^{4}

Multiply

More Steps

Evaluate

7 a \times a^{4}

Multiply the terms with the same base by adding their exponents

7 a^{1 + 4}

Add the numbers

7 a^{5}

7 a^{5} - a^{4}

Rewrite the expression

a^{4} \times 7 a - a^{4}

Solution

a^{4} (7 a - 1)

Show Solution

a_{1} = 0, a_{2} = \frac{1}{7}

Alternative Form

a_{1} = 0, a_{2} = 0. \dot{1} 4285 \dot{7}

Evaluate

7 a (a^{4}) - (a^{4})

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

7 a (a^{4}) - (a^{4}) = 0

Calculate

7 a \times a^{4} - (a^{4}) = 0

Calculate

7 a \times a^{4} - a^{4} = 0

Multiply

More Steps

Multiply the terms

7 a \times a^{4}

Multiply the terms with the same base by adding their exponents

7 a^{1 + 4}

Add the numbers

7 a^{5}

7 a^{5} - a^{4} = 0

Factor the expression

a^{4} (7 a - 1) = 0

Separate the equation into 2 possible cases

a^{4} = 0 7 a - 1 = 0

The only way a power can be 0 is when the base equals 0

a = 0 7 a - 1 = 0

Solve the equation

More Steps

Evaluate

7 a - 1 = 0

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

7 a = 0 + 1

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

7 a = 1

Divide both sides

\frac{7 a}{7} = \frac{1}{7}

Divide the numbers

a = \frac{1}{7}

a = 0 a = \frac{1}{7}

Solution

a_{1} = 0, a_{2} = \frac{1}{7}

Alternative Form

a_{1} = 0, a_{2} = 0. \dot{1} 4285 \dot{7}

Show Solution