Solve (a^2 a^3 a^4)^-2

Question

Simplify the expression

\frac{1}{a ^{18}}

Evaluate

(a^{2} \times a^{3} \times a^{4})^{- 2}

Multiply

More Steps

Multiply the terms

a^{2} \times a^{3} \times a^{4}

Multiply the terms with the same base by adding their exponents

a^{2 + 3 + 4}

Add the numbers

a^{9}

(a^{9})^{- 2}

Transform the expression

a^{9 (- 2)}

Multiply the numbers

More Steps

Evaluate

9 (- 2)

Multiplying or dividing an odd number of negative terms equals a negative

- 9 \times 2

Multiply the numbers

- 18

a^{- 18}

Solution

\frac{1}{a ^{18}}

Show Solution

a \in \emptyset

Evaluate

(a^{2} \times a^{3} \times a^{4})^{- 2}

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

(a^{2} \times a^{3} \times a^{4})^{- 2} = 0

Find the domain

More Steps

Evaluate

a^{2} \times a^{3} \times a^{4} \neq = 0

Multiply

More Steps

Evaluate

a^{2} \times a^{3} \times a^{4}

Multiply the terms with the same base by adding their exponents

a^{2 + 3 + 4}

Add the numbers

a^{9}

a^{9} \neq = 0

The only way a power can not be 0 is when the base not equals 0

a \neq = 0

(a^{2} \times a^{3} \times a^{4})^{- 2} = 0, a \neq = 0

Calculate

(a^{2} \times a^{3} \times a^{4})^{- 2} = 0

Multiply

More Steps

Multiply the terms

a^{2} \times a^{3} \times a^{4}

Multiply the terms with the same base by adding their exponents

a^{2 + 3 + 4}

Add the numbers

a^{9}

(a^{9})^{- 2} = 0

Evaluate the power

More Steps

Evaluate

(a^{9})^{- 2}

Transform the expression

a^{9 (- 2)}

Multiply the numbers

More Steps

Evaluate

9 (- 2)

Multiplying or dividing an odd number of negative terms equals a negative

- 9 \times 2

Multiply the numbers

- 18

a^{- 18}

a^{- 18} = 0

Rewrite the expression

\frac{1}{a ^{18}} = 0

Cross multiply

1 = a^{18} \times 0

Simplify the equation

1 = 0

Solution

a \in \emptyset

Show Solution