Multiply Powers of 11: Simplifying 11²×11³×11⁴

Question

Simplify the following equation:

112×113×114= 11^2\times11^3\times11^4=

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)
00:08 equals the same base raised to the sum of the exponents (N+M)
00:12 We will apply this formula to our exercise
00:18 We'll maintain the base and add up the exponents
00:29 This is the solution

Step-by-Step Solution

To solve this problem, we will simplify the expression 112×113×114 11^2 \times 11^3 \times 11^4 by using the multiplication rule of exponents.

  • Step 1: Identify that all the bases are the same, which is 11.

  • Step 2: Apply the exponent multiplication rule: am×an=am+n a^m \times a^n = a^{m+n} .

Now, apply this rule:

112×113×114=112+3+4 11^2 \times 11^3 \times 11^4 = 11^{2+3+4}

Calculate the sum of the exponents:

2+3+4=9 2 + 3 + 4 = 9

Thus, the expression simplifies to:

119 11^9

Therefore, the simplified version of the expression is:

112+3+4=119 11^{2+3+4} = 11^9

Upon reviewing the choices provided, the correct choice for the simplified expression is choice 3: 112+3+4 11^{2+3+4} .

Answer

112+3+4 11^{2+3+4}