Which expression is correctly developed to use the Power Rule of Exponents?(1 point)
Responses
(74)8
left parenthesis 7 superscript 4 baseline right parenthesis superscript 8 baseline
(−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
129
None of the given options correctly use the Power Rule of Exponents. The Power Rule states that to raise a power to another power, you multiply the exponents. Therefore, the correct expression using the Power Rule would be:
(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
102
10 superscript 2 baseline
1063
10 superscript 63 baseline
1016
The correct answer is
(10^9)^7 = 10^(9*7) = 10^63
Therefore, the corresponding option is:
1063
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
(45)2
left parenthesis 4 superscript 5 baseline right parenthesis squared
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
154
15 superscript 4 baseline
158
The correct answer is:
(15^6)^2 = 15^(6*2) = 15^12
Therefore, the corresponding option is:
1512
What exponent would make the two expressions equivalent: (33)x=324?(1 point)
Responses
8
8
15
15
21
21
27
27
To find the exponent that would make the two expressions equivalent, we can set up an equation:
(3^3)^x = 324
Raising 3^3 to the power of x is the same as raising 3 to the power of 3x:
3^(3x) = 324
To solve for x, we can take the logarithm of both sides:
log(3^(3x)) = log(324)
Using the power rule of logarithms, we can bring down the exponent:
3x * log(3) = log(324)
Now we can solve for x by dividing both sides by log(3):
3x = log(324) / log(3)
Using a calculator, we can find:
3x ≈ 4.055
To solve for x, we can divide by 3:
x ≈ 4.055 / 3 ≈ 1.352
Therefore, the exponent that would make the two expressions equivalent is approximately 1.352.
None of the provided responses match the correct answer.
can you find a solution?
Apologies for the confusion earlier. Let's solve the equation (3^3)^x = 324.
(3^3)^x can be simplified to 27^x.
We are looking for an exponent x such that 27^x equals 324.
To find x, we can take the logarithm of both sides:
log(27^x) = log(324)
Using the logarithmic property, we can bring down the exponent:
x * log(27) = log(324)
Now we can solve for x by dividing both sides by log(27):
x = log(324) / log(27)
Using a calculator, we can find:
x ≈ 2
Therefore, the exponent that makes the two expressions equivalent is 2.