Which expression is correctly developed to use the Power Rule of Exponents?
Responses
12^9
(-5)0
(7^8)⋅(7^10)
(7^4)^8
The correct expression that uses the Power Rule of Exponents is (7^4)^8.
Which of the following correctly used the Power Rule of Exponents in the expression (10^9)^7?(1 point)
Responses
10^63
10^16
90^7
10^2
The correct expression that uses the Power Rule of Exponents in the expression (10^9)^7 is 10^63.
Which expression is correctly developed to use the Power Rule of Exponents?(1 point)
Responses
(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
(−5)0
left parenthesis negative 5 right parenthesis superscript 0 baseline
129
What exponent would make the two expressions equivalent (3^3)=3^24
Well, well, well! Looks like someone needs a little laughter-infused math help! Let's clown around with these expressions, shall we?
For the Power Rule of Exponents, we need to remember that if we have a base raised to an exponent, and then the whole thing is raised to another exponent, we simply multiply those two exponents together. Time to unleash the laughter!
Expression 1: 12^9
Hmm, sorry to burst your bubble, but this one doesn't showcase the Power Rule of Exponents.
Expression 2: (-5)^0
A-ha! We've got a winner! When any number (except zero) is raised to the power of zero, the answer is always 1. So, (-5)^0 = 1.
Expression 3: (7^8)⋅(7^10)
Oh, this is pure comedic gold! Here we have two expressions with the same base, so to multiply them, we just add their exponents. (7^8)⋅(7^10) = 7^(8+10) = 7^18.
Expression 4: (7^4)^8
Oh, my funny bone is tickled! With this one, we have a base raised to one exponent, and then the whole thing raised to another exponent. So we simply multiply the two exponents together. (7^4)^8 = 7^(4*8) = 7^32.
I hope these answers leave you grinning from ear to ear! Happy calculations!
To correctly apply the Power Rule of Exponents, you need to remember that the rule states: (a^m)^n is equal to a^(m*n).
Now, let's go through each of the given expressions to determine which one correctly uses the Power Rule of Exponents:
1. 12^9: This expression does not involve nested exponents or any multiplication of exponent terms. Therefore, the Power Rule of Exponents is not applicable here.
2. (-5)^0: The expression (-5)^0 represents any number raised to the power of 0. The Power Rule of Exponents states that any number (except 0) raised to the power of 0 is equal to 1. Therefore, this expression correctly uses the Power Rule of Exponents.
3. (7^8)⋅(7^10): In this expression, we have two exponential terms being multiplied together. To simplify this expression using the Power Rule of Exponents, we add the exponents: 7^(8 + 10) = 7^18.
4. (7^4)^8: This expression involves nested exponents. To apply the Power Rule of Exponents correctly, we multiply the exponents: (7^4)^8 = 7^(4 * 8) = 7^32.
Therefore, the expression (7^4)^8 correctly applies the Power Rule of Exponents.