Use the Product Rule of Exponents to simplify the expression 24 ⋅22 .
To simplify the expression 24 ⋅22 using the product rule of exponents, we add the exponents together:
24 ⋅ 22 = 2^4 ⋅ 2^2 = 2^(4+2) = 2^6
So, 24 ⋅22 simplifies to 2^6.
Question
Use the Product Rule of Exponents to simplify the expression 3
6^8 ⋅3^3 .
To simplify the expression 6^8 ⋅ 3^3 using the product rule of exponents, we add the exponents together:
6^8 ⋅ 3^3 = (2^3)^8 ⋅ 3^3 = 2^(3*8) ⋅ 3^3 = 2^24 ⋅ 3^3
So, 6^8 ⋅ 3^3 simplifies to 2^24 ⋅ 3^3.
Use the Product Rule of Exponents to simplify the expression 75 ⋅72
To simplify the expression 75 ⋅ 72 using the product rule of exponents, we need to rewrite the numbers in terms of their prime factorization:
75 = 3^1 ⋅ 5^2
72 = 2^3 ⋅ 3^2
Now we can use the product rule of exponents to simplify:
75 ⋅ 72 = (3^1 ⋅ 5^2) ⋅ (2^3 ⋅ 3^2)
Since the bases are different (3 and 2), we cannot simplify further using the product rule of exponents. Therefore, the expression 75 ⋅ 72 cannot be further simplified.
Which expression is correctly developed to use the Product Rule of Exponents?(1 point)
Responses
(52)9
left parenthesis 5 squared right parenthesis superscript 9 baseline
62⋅73
6 squared times 7 cubed
108⋅108
10 superscript 8 baseline times 10 superscript 8 baseline
327
The expression that is correctly developed to use the Product Rule of Exponents is 62⋅73 (6 squared times 7 cubed).
Which of the following correctly used the Product Rule of Exponents to simplify the expression 1008⋅1007?(1 point)
Responses
10015
100 superscript 15 baseline
10056
100 superscript 56 baseline
20015
200 superscript 15 baseline
10,00015
To simplify the expression 1008⋅1007 using the Product Rule of Exponents, we add the exponents together:
1008 = 2^4 ⋅ 3^2 ⋅ 7^1
1007 = 2^0 ⋅ 3^0 ⋅ 7^1
By multiplying the bases together separately, we can use the Product Rule of Exponents:
1008⋅1007 = 2^4 ⋅ 2^0 ⋅ 3^2 ⋅ 3^0 ⋅ 7^1 ⋅ 7^1 = 2^(4+0) ⋅ 3^(2+0) ⋅ 7^(1+1) = 2^4 ⋅ 3^2 ⋅ 7^2
Therefore, the correct expression that uses the Product Rule of Exponents to simplify 1008⋅1007 is 20015 (200 superscript 15 baseline).
Find the numerical equivalent of 102 ⋅103(1 point)
Responses
100,000
100,000
105
10 superscript 5 baseline
10
10
1,100