Which expression is correctly developed to use the Power Rule of Exponents?(1 point)
Responses
(−5)0
left parenthesis negative 5 right parenthesis superscript 0 baseline
(78)⋅(710)
left parenthesis 7 superscript 8 baseline right parenthesis times left parenthesis 7 superscript 10 baseline right parenthesis
(74)8
left parenthesis 7 superscript 4 baseline right parenthesis superscript 8 baseline
129
(−5)0
left parenthesis negative 5 right parenthesis superscript 0 baseline
(78)⋅(710)
left parenthesis 7 superscript 8 baseline right parenthesis times left parenthesis 7 superscript 10 baseline right parenthesis
(74)8
left parenthesis 7 superscript 4 baseline right parenthesis superscript 8 baseline
129
The expression that is correctly developed to use the Power Rule of Exponents is (7^4)^8.
Which of the following correctly used the Power Rule of Exponents in the expression (109)7 ?(1 point)
Responses
907
90 superscript 7 baseline
1063
10 superscript 63 baseline
1016
10 superscript 16 baseline
102
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
(42)8
left parenthesis 4 squared right parenthesis superscript 8 baseline
(412)2
left parenthesis 4 superscript 12 baseline right parenthesis squared
4⋅4⋅4⋅4⋅4⋅4⋅4
4 times 4 times 4 times 4 times 4 times 4 times 4
(45)2
The equivalent expanded expression of 4^10 using the Power Rule of Exponents is 4⋅4⋅4⋅4⋅4⋅4⋅4⋅4⋅4⋅4.
Use the Power Rule of Exponents to create an expression equivalent to (156)2 .(1 point)
Responses
153
15 cubed
1512
15 superscript 12 baseline
158
15 superscript 8 baseline
154
The expression that is equivalent to (156)^2 using the Power Rule of Exponents is (15)^12.
What exponent would make the two expressions equivalent: (33)x=324 ?(1 point)
Responses
27
15
21
8
To find the exponent that would make the two expressions equivalent, we need to solve the equation (33)^x = 324.
Taking the logarithm of both sides, we have x*log(33) = log(324).
Now, dividing both sides by log(33), we get x = log(324) / log(33).
Calculating this expression, we find that x ≈ 1.504.
Rounding to the nearest whole number, the exponent that would make the two expressions equivalent is 2 (since 2 is the closest whole number to 1.504). Therefore, the correct answer is 2.