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
(7^8)⋅(7^10)
left parenthesis 7 superscript 8 baseline right parenthesis times left parenthesis 7 superscript 10 baseline right parenthesis
(7^4)^8
left parenthesis 7 superscript 4 baseline right parenthesis superscript 8 baseline
12^9
Twelve superscript 9 baseline
Which of the following correctly used the Power Rule of Exponents in the expression (10^9)^7?(1 point)
Responses
10^63
10 superscript 63 baseline
10^16
10 superscript 16 baseline
90^7
90 superscript 7 baseline
10^2
10 superscript 63 baseline
If the expression 410 was simplified using the Power Rule of Exponents, what is an equivalent expanded expression? (1 point)
Responses
(4^5)^2
left parenthesis 4 superscript 5 baseline right parenthesis squared
(4^2)^8
left parenthesis 4 squared right parenthesis superscript 8 baseline
(4^12)^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
(4^5)^2
Use the Power Rule of Exponents to create an expression equivalent to (15^6)^2.(1 point)
Responses
15^4
15 superscript 4 baseline
15^8
15 superscript 8 baseline
15^12
15 superscript 12 baseline
15^3
15 cubed
(15^6)^2 = 15^(6*2) = 15^12
What exponent would make the two expressions equivalent: (3^3)x=3^24?(1 point)
Responses
8
8
21
21
27
27
15
15
To find the exponent that would make the two expressions equivalent, we can set the exponents equal to each other:
3^3x = 3^24
Since the bases (3) are the same, we can equate the exponents:
3x = 24
Now we can solve for x:
x = 24/3
x = 8
Therefore, the exponent that would make the two expressions equivalent is 8.
To correctly use the Power Rule of Exponents, we need to understand that the rule states that when we have an exponent raised to another exponent, we multiply the exponents.
Now, let's analyze each of the expressions provided:
1. (−5)^0: This expression represents a negative 5 raised to the 0 power. According to the Power Rule, any number (except for zero) raised to the 0 power equals 1. Therefore, the correct development of this expression is 1.
2. (7^8)⋅(7^10): This expression involves two exponents being multiplied. According to the Power Rule, when we multiply two numbers with the same base, we add their exponents. So the correct development of this expression is (7^(8 + 10)) = 7^18.
3. (7^4)^8: This expression represents 7 raised to the power of 4, and that whole expression raised to the power of 8. According to the Power Rule, when we raise an exponent to another exponent, we multiply the exponents. Therefore, the correct development of this expression is 7^(4 * 8) = 7^32.
4. 12^9: This expression is already in its simplest form and does not involve any specific application of the Power Rule. Therefore, there is no development needed for this expression.
In conclusion, the expression (7^4)^8 is correctly developed to use the Power Rule of Exponents.