Question

use a pattern to rewrite the expression, and simplify the result if possible. select the correct choice and, if necessary, fill in the answer box to complete your choice.
use a pattern to rewrite the expression (2^7 cdot 2^8), and simplify the result if possible. select the correct choice and, if necessary, fill in the answer box to complete your choice.

a. (2^7 cdot 2^7 cdot 2^7 cdot 2^7 cdot 2^7 cdot 2^7 cdot 2^7 cdot 2^7), which cannot be simplified further.

b. (2^7 cdot 2^8 = (2 cdot 2 cdot 2 cdot 2 cdot 2 cdot 2 cdot 2) cdot (2 cdot 2 cdot 2 cdot 2 cdot 2 cdot 2 cdot 2 cdot 2)), which cannot be simplified further.

c. (2^7 cdot 2^8 = \frac{2 cdot 2 cdot 2 cdot 2 cdot 2 cdot 2 cdot 2}{2 cdot 2 cdot 2 cdot 2 cdot 2 cdot 2 cdot 2 cdot 2}), which simplifies to (square).
(type exponential notation with positive exponents.)

d. (2^7 cdot 2^8 = \frac{2 cdot 2 cdot 2 cdot 2 cdot 2 cdot 2 cdot 2}{2 cdot 2 cdot 2 cdot 2 cdot 2 cdot 2 cdot 2 cdot 2}), which cannot be simplified further.

e. (2^7 cdot 2^8 = 2^7 cdot 2^7 cdot 2^7 cdot 2^7 cdot 2^7 cdot 2^7 cdot 2^7 cdot 2^7), which simplifies to (square).
(type exponential notation with positive exponents.)

f. (2^7 cdot 2^8 = (2 cdot 2 cdot 2 cdot 2 cdot 2 cdot 2 cdot 2) cdot (2 cdot 2 cdot 2 cdot 2 cdot 2 cdot 2 cdot 2 cdot 2)), which simplifies to (square).

Explanation:

Step1: Recall exponent product rule

For same base $a^m \cdot a^n = a^{m+n}$

Step2: Apply rule to $2^7 \cdot 2^8$

$2^7 \cdot 2^8 = 2^{7+8}$

Step3: Calculate the exponent

$2^{7+8} = 2^{15}$

Step4: Evaluate options

Options A, B, C, D, F use incorrect operations (multiplication of exponents, repeated multiplication with wrong simplification). Option E correctly applies the product rule for exponents.

Answer:

E. $2^7 \cdot 2^8 = 2^7 \cdot 2^7 \cdot 2^7 \cdot 2^7 \cdot 2^7 \cdot 2^7 \cdot 2^7 \cdot 2^7$, which simplifies to $2^{15}$.
(Type exponential notation with positive exponents.)