Question

Simplify the variable expression. $$\left(-b^{2}\right)\left(-b^{3}\right)\left(-b^{4}\right)$$

Short answer

The simplified version of the expression \(\left(-b^{2}\right)\left(-b^{3}\right)\left(-b^{4}\right)\) is \(-b^{9}\).

Step-by-step solution

Take Care of the Negative Signs

Each term has a negative sign, and since we are multiplying three negative terms together, the product will be negative. That is because the product of an odd number of negative numbers is always negative.

Simplify the Expression with Exponent Properties

When we multiply exponential expressions with the same base, we can add the exponents. Therefore, the exponent of \(b\) will be the sum of 2, 3, and 4.

Calculate the Sum of the Exponents

Adding the exponents together gives \(2+3+4=9\). Therefore, the simplified form of the expression will have \(b^{9}\) as its variable component.

Write the Final Simplified Expression

Combine the results from steps 1 and 3 to write the final simplified expression. The final result is \(-b^{9}\) which represents the product of the three original expressions.