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

Question

Simplify the following equation:

5×58= 5\times5^8=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:04 Any number raised to the power of 1 is always equal to itself
00:08 We'll apply this formula to our exercise, and raise it to the power of 1
00:12 According to the laws of exponents, the multiplication of powers with an equal base (A)
00:15 equals the same base raised to the sum of the exponents (N+M)
00:18 We'll apply this formula to our exercise
00:22 We'll then proceed to add up the exponents and raise them to this power
00:29 This is the solution

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.

Answer

59 5^9

More Questions

Related Subjects

Multiplying Exponents with the Same Base

Question Types

Multiplication of Powers: Applying the formula