Final answer:
To express (2³)(4³) without exponents, multiply the bases to get 8 and then cube it, resulting in 8 x 8 x 8, which equals 512.
Step-by-step explanation:
The original problem asks to write an expression without exponents that is equivalent to (2³)(4³). To solve this, we need to understand how exponentiation works and how to multiply numbers with the same exponent.
Understanding Exponentiation
Exponentiation is a form of mathematical shorthand. When we have a number like 4³, it means 4 multiplied by itself three times, which is 4 x 4 x 4. Similarly, 2³ is 2 x 2 x 2.
Multiplying Numbers with the Same Exponents
When you multiply numbers that have the same exponents (like (2³)(4³)), you actually multiply the bases (2 and 4, in this case) first and then apply the exponent. Therefore:
- Multiply the bases: 2 * 4 = 8.
- Apply the exponent: 8³.
- Expand: 8³ = 8 x 8 x 8.
8 x 8 x 8 is the expression without exponents equivalent to (2³)(4³).
Breaking it further down:
Therefore, the simplified expression without exponents for (2³)(4³) is 512.