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
(74)8
left parenthesis 7 superscript 4 baseline right parenthesis superscript 8 baseline
(78)⋅(710)
left parenthesis 7 superscript 8 baseline right parenthesis times left parenthesis 7 superscript 10 baseline right parenthesis
129
12 superscript 9 baseline
The correct expression that uses the Power Rule of Exponents is:
(74)8
This means 7 raised to the power of 4, then the result is raised to the power of 8.
Which of the following correctly used the Power Rule of Exponents in the expression (109)7?(1 point)
Responses
102
10 superscript 2 baseline
1063
10 superscript 63 baseline
1016
10 superscript 16 baseline
907
The correct answer is:
1063
This means 10 raised to the power of 9, then the result is raised to the power of 7.
If the expression 410 was simplified using the Power Rule of Exponents, what is an equivalent expanded expression? (1 point)
Responses
4⋅4⋅4⋅4⋅4⋅4⋅4
4 times 4 times 4 times 4 times 4 times 4 times 4
(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
The correct answer is:
4⋅4⋅4⋅4⋅4⋅4⋅4
This is an equivalent expanded expression of 410. It represents multiplying 4 by itself 10 times.
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
154
15 superscript 4 baseline
158
The correct answer is:
1512
This expression is equivalent to (156)2. It means 15 raised to the power of 6, then the result is raised to the power of 2.
What exponent would make the two expressions equivalent: (33)x=324?(1 point)
Responses
27
27
15
15
8
8
21
To find the exponent that would make the two expressions equivalent, we need to solve the equation (33)x = 324.
By taking the logarithm of both sides, we can determine the value of x:
log((33)x) = log(324)
Using logarithmic properties, we can bring down the exponent and rewrite the equation as:
x * log(33) = log(324)
Now, we can solve for x:
x = log(324) / log(33)
Using a calculator, we can evaluate the logarithms and find that:
x ≈ 2.079
So, the exponent that would make the two expressions equivalent is approximately 2.079.
The Power Rule of Exponents states that when you raise a power to another power, you multiply the exponents.
In the given options, the one that correctly uses the Power Rule of Exponents is:
(74)8
This expression represents the number 7 raised to the power of 4, and then that result raised to the power of 8. To simplify this expression using the Power Rule, you can multiply the exponents:
7^4 * 8 = 7^(4 * 8) = 7^32