Question

Type the correct answer in the box. Use numerals instead of words. If necessary, use / for the fraction bar and ^ to indicate an exponent. Find the product. 5^56 × 5^22 × 5^-96 =

Answer 1

Answer:

The product of the 5^56 x 5^22 x 5^-96= 1/5^18.

Step-by-step explanation:

The problem represents the Laws of Exponents.  When you multiply using exponents, you keep the base and add the exponents.  In this case, the base is 5 and our exponents are 56 + 22 + -96.  We we add these three integers, we get a total of -18, which gives us a base of 5 and exponent of -18 or 5^-18.  We don't typically have negative exponents, so our next rule to follow is when you have negative exponents, you flip the base, or make it a fraction, and make the exponent positive.  This gives us a final answer of 1/5^18.  

Answer 2

The value of the product is 5^56 × 5^22 × 5^(-96) is 1/(5^18)

Laws of Exponents:

• By the Product property of Laws of exponents,

         While multiplying two exponents with the same base then we should add the powers to get the result.

            Example: x^a + x^b = x^(a+b)

• Here the product 5^56 × 5^22 × 5^(-96) can be expressed as

              5^56 × 5^22 × 5^-96 = 5^(56+22+(-96))

                                                    = 5^(-18)

• By the Negative property of laws of exponents,

       A non-zero real number with negative power is written as

    1/ (non-zero number with the positive power of the same number).

     Example:  x^(-2) = 1/(x^2)

  So, we can write 5^(-18) as 1/5^(18).

   Hence,

       5^56 × 5^22 × 5^-96 = 1/5^(18).

Know more about the Bases and  exponents:

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