Question

Use multiplication to fully expand the expression below. a, b, to the power 4 ab 4 Answer Attempt 1 out of 2 Press the dot⋅ button or type the * symbol on your keyboard to represent multiplication. Using times× for multiplication is inappropriate when xx may be used as a variable. Expanded form:

Answer 1

When expanding the expression a^4 times ab^4, we use the rule of multiplying exponentiated quantities to add the exponents for the common base 'a'. This results in a^8 times b^4, with the exponent 4 applying to both 'a' and 'b' in (ab)^4.

Step-by-step explanation:

Multiplication of Exponentiated Quantities

To fully expand the expression a to the power of 4 times ab to the power of 4, we must first understand the properties of exponents. When we multiply exponentiated quantities with the same base, we add the exponents. In this case, a is raised to the fourth power, and ab is also raised to the fourth power, so we effectively have:

• (a^4) × (ab)^4
• (a^4) × (a^4 × b^4)
• a^4 × a^4 × b^4

According to the multiplication rule for exponentials, we multiply the digit terms as usual and add the exponents of the exponential terms. Thus:

• (a^4) × (a^4) = a^(4+4)
  • a^(4+4) = a^8

For the expanded form:

• a^8 × b^4

This is because the exponent 4 applies to both a and b in the term (ab)^4.