Simplify the Expression: 8³ × 8 Using Exponent Rules

Question

Simplify the following equation:

83×8= 8^3\times8=

Video Solution

Solution Steps

00:05 Let's simplify this problem together.
00:08 Remember, any number to the power of 1 is just itself.
00:13 Let's use this idea in our exercise.
00:16 When multiplying powers with the same base, A
00:21 simply add the exponents. It becomes A to the power of N plus M.
00:27 Let's apply this rule now.
00:29 We'll add the exponents and set that as our new power.
00:33 And that's how we solve it! Great job!

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}