Problem 44 - College Algebra Essentials

Question

Simplify each exponential expression. $$\left(-3 x^{4} y^{6}\right)^{3}$$

Step-by-Step Solution

Answer

The simplified exponential expression is \(-27x^{12}y^{18}\)

Step 1: Identify the expression

The expression given is \(\left(-3x^{4}y^{6}\right)^{3}\). This expression means -3 raised to the third power, x to the power of 4 raised to the third power, and y to the power of 6 raised to the third power.

Step 2: Apply exponentiation rules

We know that when raising a power to another power, we multiply the exponents. Applying this rule, we get \(-3^{3}(x^{4*3})(y^{6*3}) = -3^{3}x^{12}y^{18}\)

Step 3: Evaluate the exponential expression

Now evaluate \(-3^{3}\) which is \(-27\). The equation simplifies to \(-27x^{12}y^{18}\)