Which of the following correctly used the Power Rule of Exponents in the expression (10^9) ^7
10^63
90^7
10^16
10^2
The correct answer is 10^63.
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Apply the Properties of Integer Exponents to generate equivalent expressions to 3 to the power of 7 ⋅ 3 to the power of −9 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.
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To generate equivalent expressions with only positive exponents, we can use the property of negative exponents, which states that a^(-n) is equal to 1/a^n. Applying this property to 3^(-9), we get 1/3^9.
Now, let's simplify the expression:
3^7 * 1/3^9
Using the quotient rule of exponents, a^m / a^n is equal to a^(m-n), we can combine the terms with the same base:
3^(7-9) = 3^(-2)
Again, applying the property of negative exponents, we get:
1/3^2 = 1/9
Therefore, the simplified fraction with no remaining exponents is 1/9.
If the expression 4^10 was simplified using the Power Rule of Exponents, what is an equivalent expanded expression? (1 point)
Responses
4⋅4⋅4⋅4⋅4⋅4⋅4
(4^5)^2
(4^5)^2
(4^2)^8