Which expression is correctly developed to use the power rule of exponents?
A. (-5)⁰
B. (7⁸)•(7¹⁰)
C. (7⁴)⁸
D. 12⁹
The correct expression that uses the power rule of exponents is option C. (7⁴)⁸.
Which of the following correctly used the power rule of exponents in the expression (10⁹)⁷?
A. 10⁶³
B. 90⁷
C.10²
D10¹⁶
The correct answer is option A. 10⁶³.
To simplify the expression (10⁹)⁷ using the power rule of exponents, we multiply the exponents together.
(10⁹)⁷ = 10^(9*7) = 10⁶³.
If the expression 4¹⁰ was simplified using the power rule of exponents, what is an equivalent expanded expression?
A. (4²)⁸
B. (4⁵)²
C. 4•4•4•4•4•4•4
D. (4¹²)²
The correct answer is option D. (4¹²)².
To simplify the expression 4¹⁰ using the power rule of exponents, we multiply the exponents together.
4¹⁰ = 4^(1*10) = 4¹².
Therefore, an equivalent expanded expression would be (4¹²)².
The expression that is correctly developed to use the power rule of exponents is:
C. (7⁴)⁸
The power rule of exponents states that when you raise a power to another exponent, you multiply the exponents. The correct expression that utilizes the power rule of exponents is:
C. (7⁴)⁸
To understand why this is the correct choice, let's break it down step by step:
1. Start with the base number, 7.
2. Raise 7 to the power of 4, resulting in 7⁴.
3. Then, take the result from step 2 and raise it to the power of 8, resulting in (7⁴)⁸.
By applying the power rule of exponents, we multiply the exponents 4 and 8 to get a final exponent of 32. Thus, the correct expression using the power rule of exponents is (7⁴)⁸.