Simplify 11^10 × 11^11: Multiplying Powers with Same Base

Question

Simplify the following equation:

1110×1111= 11^{10}\times11^{11}=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 According to the laws of exponents, the multiplication of exponents with an equal base (A)
00:07 equals the same base raised to the sum of exponents (N+M)
00:11 We will apply this formula to our exercise
00:15 We will add up the exponents and raise them to this power
00:22 Let's calculate the sum of the exponents
00:26 This is the solution

Step-by-Step Solution

To solve the problem of simplifying the equation 1110×1111 11^{10} \times 11^{11} , follow these steps:

  • Step 1: Identify that the bases are the same (11).

  • Step 2: Apply the multiplication of powers rule, which states that when multiplying like bases, you add the exponents.

  • Step 3: Add the exponents: 10+11 10 + 11 .

  • Step 4: Perform the addition: 10+11=21 10 + 11 = 21 .

  • Step 5: Write the expression with the new exponent: 1110+11=1121 11^{10+11}= 11^{21} .

Therefore, the simplified expression is 1121 11^{21} . This corresponds to options 1 and 2 being correct as they represent the same expression when evaluating the sum, which is also represented by choice 4 as "a'+b' are correct".

Answer

a'+b' are correct