Multiply Powers with Base 5: Solving 5^(-8) × 5^6

Question

Insert the corresponding expression:

5−8×56= 5^{-8}\times5^6=

Video Solution

Solution Steps

00:00 Simplify the following problem
00:03 According to the laws of exponents, the multiplication of powers with the same base (A)
00:06 equals the same base raised to the sum of the exponents (N+M)
00:09 We will apply this formula to our exercise
00:13 We'll maintain the base and add the exponents together
00:20 According to the laws of exponents, any number with a negative exponent (-N)
00:24 equals its reciprocal raised to the opposite exponent (N)
00:27 We will apply this formula to our exercise
00:31 We'll convert it to the reciprocal and raise it to the opposite power
00:35 This is the solution

Step-by-Step Solution

Let's simplify the expression 5−8×565^{-8} \times 5^6 using the rules of exponents.

  • Step 1: Apply the rule for multiplying powers with the same base. According to this rule, when multiplying like bases, we add the exponents: 5−8×56=5−8+65^{-8} \times 5^6 = 5^{-8 + 6}
  • Step 2: Calculate the sum of the exponents: −8+6=−2-8 + 6 = -2.
  • Step 3: Write the simplified expression: 5−25^{-2}.
  • Step 4: Relate the expression to the given choices:

The simplified expression 5−25^{-2} corresponds to choice 1. Additionally, rewriting a negative exponent using the fraction format gives: 5−2=1525^{-2} = \frac{1}{5^2}, which matches choice 2.

Thus, both choices 'a: 5−25^{-2}' and 'b: 152\frac{1}{5^2}' are correct.

Therefore, according to the given answer choice, a'+b' are correct.

Answer

a'+b' are correct

More Questions

Related Subjects

Multiplying Exponents with the Same Base

Question Types

Multiplication of Powers: Presenting powers with negative exponents as fractions Multiplication of Powers: Calculating powers with negative exponents