Solve the expression 15 ⋅ 8^0/5 + 4(7^0−6). (1 point)
15 ⋅ 8^0/5 + 4(7^0−6) =
15 ⋅ 8^0/5 + 4(7^0−6) = 15 ⋅ 1/5 + 4(1−6) = 15/5 + 4(-5) = 3 + (-20) = -17
Use the Power Rule of Exponents to simplify (10^3)^6
According to the power rule of exponents, when a power is raised to another power, we multiply the exponents. Therefore, (10^3)^6 can be simplified as 10^(3*6) which is equal to 10^18.
If the expression 7^15 was simplified using the Power Rule of Exponents, which of the following would be an expanded equivalent expression? (1 point)
(7^10)^5
(7^18)^3
(7⋅7⋅7) ⋅ (7⋅7⋅7) ⋅ (7⋅7⋅7) ⋅ (7⋅7⋅7) ⋅ (7⋅7⋅7)
(7⋅7⋅7⋅7⋅7)^10
The correct expanded equivalent expression would be (7⋅7⋅7⋅7⋅7)^10.
According to the Power Rule of Exponents, when a power is raised to another power, we multiply the exponents. In this case, 7^15 can be expanded as (7^5)^3 which is equal to (7⋅7⋅7⋅7⋅7)^3.
Therefore, the correct expanded equivalent expression for 7^15 using the Power Rule of Exponents is (7⋅7⋅7⋅7⋅7)^10.
Use the Power Rule of Exponents to create a simplified equivalent expression for (19^4)^9.
According to the power rule of exponents, when a power is raised to another power, we multiply the exponents. Therefore, (19^4)^9 can be simplified as 19^(4*9) which is equal to 19^36.
Apply the Property of Negative Integer Exponents to solve 7^−3. The answer should not contain any exponent expression or decimals. (1 point)
7^−3 =
The Property of Negative Integer Exponents states that a negative exponent can be rewritten as the reciprocal of the base raised to the positive exponent.
Therefore, 7^(-3) can be written as 1 / 7^(3).
So, 7^(-3) = 1 / (7^3) = 1 / (7 * 7 * 7) = 1 / 343.
Hence, the simplified expression for 7^(-3) without any exponent expression or decimals is 1/343.