Question

Which of the following is equivalent to ((2^3)(2^2)(2^4)(2^8)(2^16)(2^32)(2^64))?

a) (3^127 ⋅ 2^127)
b) (3^127 ⋅ 2^127 ⋅ 2 ⋅ 3^63 ⋅ 3 ⋅ 2^63)
c) (3^128 - 2^128)
d) (3^128 ⋅ 2^128)

Answer 1

None of the provided options are equivalent to the expression ((2^3)(2^2)(2^4)(2^8)(2^16)(2^32)(2^64)), which simplifies to 2^129. When multiplying powers with the same base, the exponents are added together.

Step-by-step explanation:

To find which expression is equivalent to ((2^3)(2^2)(2^4)(2^8)(2^16)(2^32)(2^64)), we should first recognize that when we multiply powers with the same base, we add the exponents. Let's apply this rule to simplify the given expression:

• 2^3 × 2^2 × 2^4 × 2^8 × 2^16 × 2^32 × 2^64 = 2(3+2+4+8+16+32+64)
• 2(3+2+4+8+16+32+64) = 2^129

Now, we look at the options provided to see which one corresponds to 2^129.

• (a) 3127 × 2127
• (b) 3127 × 2127 × 2 × 363 × 3 × 263
• (c) 3128 - 2128
• (d) 3128 × 2128

Since 2129 does not appear in any of the options as is, none of them are equivalent to the given expression. Each of the answers adds, multiplies, or subtracts by a power of 3, which does not align with our result of 2129. Therefore, the correct equivalent expression is not listed among the options given.