Simplify 5×5^8: Solving an Exponential Multiplication Problem

Simplify the following equation:

5×58= 5\times5^8=

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:07 Let's simplify this problem together.
00:11 Any number raised to the power of one, equals the number itself.
00:17 We'll use this idea and raise our exercise to the power of one.
00:21 Now, when multiplying powers with the same base, A, you add the exponents.
00:27 This means A to the power of N plus M.
00:31 Let's apply this to our exercise.
00:34 We'll add the exponents, then raise the base to this new power.
00:39 And there you have it! That's how we solve this problem.

Step-by-step written solution

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1

Understand the problem

Simplify the following equation:

5×58= 5\times5^8=

2

Step-by-step solution

To solve the problem of simplifying 5×585 \times 5^8, we use the rules of exponents:

  • Identify that 55 can be rewritten as 515^1.
  • Apply the multiplication of powers rule: am×an=am+na^m \times a^n = a^{m+n}.
  • Add the exponents: 1+8=91 + 8 = 9.
  • Thus, 51×58=51+8=595^1 \times 5^8 = 5^{1+8} = 5^9.

Therefore, the simplified form of the given expression is 595^9.

Hence, the correct answer is choice : 595^9.

3

Final Answer

59 5^9

Practice Quiz

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\( 112^0=\text{?} \)

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