Which of the following is using the Product Rule for Exponents correctly?(1 point)
Responses
53×57=521
5 cubed times 5 to the 7th power is equal to 5 to the 21th power
126×12−5=12
12 to the 6th power times 12 to the negative 5 power is equal to 12
82×810=1612
8 squared times 8 to the 10th power is equal to 16 to the 12th power
326×323=323
None of the given options are using the Product Rule for Exponents correctly.
Simplify using the Product Rule of Exponents: 93×95×9−2=
(1 point)
Responses
276
27 to the 6th power
9−30
9 to the negative 30 power
96
9 to the 6th power
none of the above. This can't be simplified.
To simplify using the Product Rule of Exponents, we add the exponents when multiplying powers of the same base. Therefore, we have 9^3 × 9^5 × 9^(-2) = 9^(3 + 5 + (-2)) = 9^6.
The correct response is: 9 to the 6th power.
The correct use of the Product Rule for Exponents is:
82 × 810 = 1612
This shows that 8 squared (82) times 8 to the 10th power (810) is equal to 16 to the 12th power (1612).