Solve 1x^5*-6^0 5x^4*-6^1 10x^3*-6^2 10x^2*-6^3 5x^1*

Question

Simplify the expression

2500 \times 6^{11} x^{20}

Evaluate

1 \times x^{5} (- 6^{0}) \times 5 x^{4} (- 6^{1}) \times 10 x^{3} (- 6^{2}) \times 10 x^{2} (- 6^{3}) \times 5 x^{1} (- 6^{4}) \times 1 \times x^{0} (- 6) x^{5}

Evaluate the power

1 \times x^{5} (- 1) \times 5 x^{4} (- 6^{1}) \times 10 x^{3} (- 6^{2}) \times 10 x^{2} (- 6^{3}) \times 5 x^{1} (- 6^{4}) \times 1 \times x^{0} (- 6) x^{5}

Evaluate

1 \times x^{5} (- 1) \times 5 x^{4} (- 6^{1}) \times 10 x^{3} (- 6^{2}) \times 10 x^{2} (- 6^{3}) \times 5 x (- 6^{4}) \times 1 \times x^{0} (- 6) x^{5}

Evaluate the power

1 \times x^{5} (- 1) \times 5 x^{4} (- 6) \times 10 x^{3} (- 6^{2}) \times 10 x^{2} (- 6^{3}) \times 5 x (- 6^{4}) \times 1 \times x^{0} (- 6) x^{5}

Evaluate the power

1 \times x^{5} (- 1) \times 5 x^{4} (- 6) \times 10 x^{3} (- 6^{2}) \times 10 x^{2} (- 6^{3}) \times 5 x (- 6^{4}) \times 1 \times 1 \times (- 6) x^{5}

Rewrite the expression

x^{5} (- 1) \times 5 x^{4} (- 6) \times 10 x^{3} (- 6^{2}) \times 10 x^{2} (- 6^{3}) \times 5 x (- 6^{4}) (- 6) x^{5}

Any expression multiplied by 1 remains the same

x^{5} \times 5 x^{4} \times 6 \times 10 x^{3} \times 6^{2} \times 10 x^{2} \times 6^{3} \times 5 x \times 6^{4} \times 6 x^{5}

Multiply the terms with the same base by adding their exponents

x^{5 + 4 + 3 + 2 + 1 + 5} \times 5 \times 6 \times 10 \times 6^{2} \times 10 \times 6^{3} \times 5 \times 6^{4} \times 6

Add the numbers

x^{20} \times 5 \times 6 \times 10 \times 6^{2} \times 10 \times 6^{3} \times 5 \times 6^{4} \times 6

Multiply the terms

More Steps

Evaluate

5 \times 10 \times 10 \times 5

Multiply the terms

50 \times 10 \times 5

Multiply the terms

500 \times 5

Multiply the numbers

2500

x^{20} \times 2500 \times 6 \times 6^{2} \times 6^{3} \times 6^{4} \times 6

Multiply the terms with the same base by adding their exponents

x^{20} \times 2500 \times 6^{1 + 2 + 3 + 4 + 1}

Add the numbers

x^{20} \times 2500 \times 6^{11}

Use the commutative property to reorder the terms

2500 x^{20} \times 6^{11}

Solution

2500 \times 6^{11} x^{20}

Show Solution

Find the roots

x \in \emptyset

Evaluate

1 \times x^{5} (- 6^{0}) \times 5 x^{4} (- 6^{1}) \times 10 x^{3} (- 6^{2}) \times 10 x^{2} (- 6^{3}) \times 5 x^{1} (- 6^{4}) \times 1 \times x^{0} (- 6) x^{5}

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

1 \times x^{5} (- 6^{0}) \times 5 x^{4} (- 6^{1}) \times 10 x^{3} (- 6^{2}) \times 10 x^{2} (- 6^{3}) \times 5 x^{1} (- 6^{4}) \times 1 \times x^{0} (- 6) x^{5} = 0

Find the domain

1 \times x^{5} (- 6^{0}) \times 5 x^{4} (- 6^{1}) \times 10 x^{3} (- 6^{2}) \times 10 x^{2} (- 6^{3}) \times 5 x^{1} (- 6^{4}) \times 1 \times x^{0} (- 6) x^{5} = 0, x \neq = 0

Calculate

1 \times x^{5} (- 6^{0}) \times 5 x^{4} (- 6^{1}) \times 10 x^{3} (- 6^{2}) \times 10 x^{2} (- 6^{3}) \times 5 x^{1} (- 6^{4}) \times 1 \times x^{0} (- 6) x^{5} = 0

Evaluate the power

1 \times x^{5} (- 1) \times 5 x^{4} (- 6^{1}) \times 10 x^{3} (- 6^{2}) \times 10 x^{2} (- 6^{3}) \times 5 x^{1} (- 6^{4}) \times 1 \times x^{0} (- 6) x^{5} = 0

Evaluate the power

1 \times x^{5} (- 1) \times 5 x^{4} (- 6) \times 10 x^{3} (- 6^{2}) \times 10 x^{2} (- 6^{3}) \times 5 x^{1} (- 6^{4}) \times 1 \times x^{0} (- 6) x^{5} = 0

Evaluate the power

1 \times x^{5} (- 1) \times 5 x^{4} (- 6) \times 10 x^{3} (- 6^{2}) \times 10 x^{2} (- 6^{3}) \times 5 x (- 6^{4}) \times 1 \times x^{0} (- 6) x^{5} = 0

Evaluate the power

1 \times x^{5} (- 1) \times 5 x^{4} (- 6) \times 10 x^{3} (- 6^{2}) \times 10 x^{2} (- 6^{3}) \times 5 x (- 6^{4}) \times 1 \times 1 \times (- 6) x^{5} = 0

Multiply the terms

More Steps

Multiply the terms

1 \times x^{5} (- 1) \times 5 x^{4} (- 6) \times 10 x^{3} (- 6^{2}) \times 10 x^{2} (- 6^{3}) \times 5 x (- 6^{4}) \times 1 \times 1 \times (- 6) x^{5}

Rewrite the expression

x^{5} (- 1) \times 5 x^{4} (- 6) \times 10 x^{3} (- 6^{2}) \times 10 x^{2} (- 6^{3}) \times 5 x (- 6^{4}) (- 6) x^{5}

Any expression multiplied by 1 remains the same

x^{5} \times 5 x^{4} \times 6 \times 10 x^{3} \times 6^{2} \times 10 x^{2} \times 6^{3} \times 5 x \times 6^{4} \times 6 x^{5}

Multiply the terms with the same base by adding their exponents

x^{5 + 4 + 3 + 2 + 1 + 5} \times 5 \times 6 \times 10 \times 6^{2} \times 10 \times 6^{3} \times 5 \times 6^{4} \times 6

Add the numbers

x^{20} \times 5 \times 6 \times 10 \times 6^{2} \times 10 \times 6^{3} \times 5 \times 6^{4} \times 6

Multiply the terms

More Steps

Evaluate

5 \times 10 \times 10 \times 5

Multiply the terms

50 \times 10 \times 5

Multiply the terms

500 \times 5

Multiply the numbers

2500

x^{20} \times 2500 \times 6 \times 6^{2} \times 6^{3} \times 6^{4} \times 6

Multiply the terms with the same base by adding their exponents

x^{20} \times 2500 \times 6^{1 + 2 + 3 + 4 + 1}

Add the numbers

x^{20} \times 2500 \times 6^{11}

Use the commutative property to reorder the terms

2500 x^{20} \times 6^{11}

Multiply the numbers

2500 \times 6^{11} x^{20}

2500 \times 6^{11} x^{20} = 0

Rewrite the expression

x^{20} = 0

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

x = 0

Check if the solution is in the defined range

x = 0, x \neq = 0

Solution

x \in \emptyset

Show Solution