Which of the following correctly used the Power Rule of Exponents in the expression (109)7?(1 point)
Responses
907
90 superscript 7 baseline
1016
10 superscript 16 baseline
102
10 superscript 2 baseline
1063
10 superscript 63 baseline
The correct answer is 10^63.
If the expression 410 was simplified using the Power Rule of Exponents, what is an equivalent expanded expression? (1 point)
Responses
(412)2
left parenthesis 4 superscript 12 baseline right parenthesis squared
(45)2
left parenthesis 4 superscript 5 baseline right parenthesis squared
(42)8
left parenthesis 4 squared right parenthesis superscript 8 baseline
4⋅4⋅4⋅4⋅4⋅4⋅4
4 times 4 times 4 times 4 times 4 times 4 times 4
The correct answer is (4^5)^2, which is equivalent to (45)^2.
The correct usage of the Power Rule of Exponents in the expression (109)7 is 10^63.
To correctly apply the Power Rule of Exponents in the expression (109)7, we need to multiply the exponent by the power inside the parentheses. The Power Rule states that raising a power to another power means multiplying the exponents together.
In this case, we have (10^9)^7. To apply the rule, we multiply 9 and 7 to get the final exponent. So, the correct answer is 10^(9*7) = 10^63.
Therefore, the correct response is:
1063
10 superscript 63 baseline