Question

Multiply the expressions and simplify: 7x⁹ * 3y * 2y⁴x⁶

Answer 1

To multiply 7x⁹ * 3y * 2y⁴x⁶, multiply the constants to get 42 and add the exponents of like bases to obtain 42x¹⁵y⁵ as the simplified expression.

Step-by-step explanation:

When multiplying expressions, especially those involving exponents, some key rules we use are:

• Multiplication of Exponentials: Multiply the digit terms in the usual way and add the exponents of the exponential terms when the bases are the same.

To multiply and simplify the expression 7x⁹ * 3y * 2y⁴x⁶, we follow these steps:

1. Multiply the constants (numbers without variables): 7 * 3 * 2 = 42.
2. Add the exponents of x because the bases are the same: x⁹ * x⁶ = x¹⁵ (since 9 + 6 = 15).
3. Multiply the y terms together: y * y⁴ = y⁵ (since the exponents add to 1 + 4 = 5).

The simplified expression is 42x¹⁵y⁵.