Simplify Powers of 2: 2³ × 2⁴ × 2⁶ × 2⁵

Question

Reduce the following equation:

23×24×26×25= 2^3\times2^4\times2^6\times2^5=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 According to the laws of exponents, the multiplication of powers with equal bases (A)
00:07 equals the same base raised to the sum of the exponents (N+M)
00:10 We will apply this formula to our exercise, each time for one multiplication
00:16 We'll maintain the base and add the exponents together
00:26 Calculate the exponents
00:32 Apply the formula once again
00:38 This is the solution

Step-by-Step Solution

To reduce the expression 23×24×26×25 2^3 \times 2^4 \times 2^6 \times 2^5 , we apply the rule of multiplication for exponents with the same base, which states that:

am×an=am+n a^m \times a^n = a^{m+n} .

Following this rule, we add up all the exponents together since they all have the same base, 2:

3+4+6+5=18 3 + 4 + 6 + 5 = 18 .

So, the expression reduces to 218 2^{18} .

Thus, the answer is 218 2^{18} .

Answer

218 2^{18}