Simplify the Expression: 8³ × 8 Using Exponent Rules

Question

Simplify the following equation:

83×8= 8^3\times8=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 Any number raised to the power of 1 is always equal to itself
00:07 Let's insert this into our exercise
00:10 According to the laws of exponents, the multiplication of powers with an equal base (A)
00:13 equals the same base raised to the sum of the exponents (N+M)
00:16 We'll apply this formula to our exercise
00:19 We'll add up the exponents and raise them to this power
00:22 This is the solution

Step-by-Step Solution

To simplify the expression 83×88^3 \times 8, we begin by identifying the implicit exponent for the standalone 8. Since there is no written exponent next to the second 8, we can assume it has an exponent of 1.

Thus, the expression can be written as:\br 83×818^3 \times 8^1.

Using the rule for multiplying powers with the same base, am×an=am+na^m \times a^n = a^{m+n}, we add the exponents:

  • Here, the base aa is 8.
  • The exponents are 3 and 1.

Therefore, 83×81=83+1=848^3 \times 8^1 = 8^{3+1} = 8^4.

Thus, the simplified expression is 84\mathbf{8^4}.

Consequently, the correct choice is 83+18^{3+1} .

Answer

83+1 8^{3+1}