Solve (x^4)^(2) (x^3)⋅(5-x)

Question

Simplify the expression

5 x^{11} - x^{12}

Evaluate

(x^{4})^{2} x^{3} (5 - x)

Multiply the exponents

x^{4 \times 2} \times x^{3} (5 - x)

Multiply the numbers

x^{8} \times x^{3} (5 - x)

Multiply the terms with the same base by adding their exponents

x^{8 + 3} (5 - x)

Add the numbers

x^{11} (5 - x)

Apply the distributive property

x^{11} \times 5 - x^{11} \times x

Use the commutative property to reorder the terms

5 x^{11} - x^{11} \times x

Solution

More Steps

Evaluate

x^{11} \times x

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{11 + 1}

Add the numbers

x^{12}

5 x^{11} - x^{12}

Show Solution

x_{1} = 0, x_{2} = 5

Evaluate

(x^{4})^{2} (x^{3}) (5 - x)

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

(x^{4})^{2} (x^{3}) (5 - x) = 0

Calculate

(x^{4})^{2} x^{3} (5 - x) = 0

Evaluate the power

More Steps

Evaluate

(x^{4})^{2}

Transform the expression

x^{4 \times 2}

Multiply the numbers

x^{8}

x^{8} \times x^{3} (5 - x) = 0

Multiply

More Steps

Multiply the terms

x^{8} \times x^{3} (5 - x)

Multiply the terms with the same base by adding their exponents

x^{8 + 3} (5 - x)

Add the numbers

x^{11} (5 - x)

x^{11} (5 - x) = 0

Separate the equation into 2 possible cases

x^{11} = 0 5 - x = 0

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

x = 0 5 - x = 0

Solve the equation

More Steps

Evaluate

5 - x = 0

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

- x = 0 - 5

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

- x = - 5

Change the signs on both sides of the equation

x = 5

x = 0 x = 5

Solution

x_{1} = 0, x_{2} = 5

Show Solution