Solve the expression 15⋅8^0/5+4(7^0−6) .(1 point)
The expression can be simplified step by step as follows:
First, let's simplify the exponents:
8^0 = 1 (Any number raised to the power of 0 equals 1)
7^0 = 1 (Same as above)
Now, we can proceed with the expression:
15⋅8^0/5+4(7^0−6)
We substitute the values for the exponents:
15⋅1/5+4(1−6)
Next, we simplify within the parentheses:
15⋅1/5+4(-5)
Multiplication and addition/subtraction are done from left to right:
3+4(-5)
Now we perform the multiplication:
3+(-20)
Finally, we add the numbers together:
3 - 20 = -17
So the final result is -17.
Use the Power Rule of Exponents to simplify (10^3)^6
The Power Rule of Exponents states that when you have an exponent raised to another exponent, you multiply the exponents.
In this case, we have (10^3)^6.
To simplify, we multiply the exponents:
10^(3*6) = 10^18
Therefore, (10^3)^6 simplifies 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)
Responses
(7⋅7⋅7⋅7⋅7)^10
left parenthesis 7 times 7 times 7 times 7 times 7 right parenthesis superscript 10 baseline
(7^18)^3
left parenthesis 7 superscript 18 baseline right parenthesis cubed
(7^10)^5
left parenthesis 7 superscript 10 baseline right parenthesis superscript 5 baseline
(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)⋅(7⋅7⋅7)
The correct expanded equivalent expression using the Power Rule of Exponents for 7^15 would be (7⋅7⋅7⋅7⋅7)^10.
This is because 7^15 means 7 raised to the power of 15, which can be written as (7⋅7⋅7⋅7⋅7)^10, where the base 7 is multiplied by itself 10 times.
Use the Power Rule of Exponents to create a simplified equivalent expression for (19^4)^9 .(1 point)
To simplify the expression (19^4)^9 using the Power Rule of Exponents, we need to multiply the exponents.
(19^4)^9 can be expanded as:
19^(4*9)
19^36
Therefore, the simplified equivalent expression for (19^4)^9 is 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)
The Property of Negative Integer Exponents states that any non-zero number raised to a negative exponent is equal to the reciprocal of the number raised to the positive exponent.
Applying this property to 7^(-3), we can rewrite it as:
1 / 7^3
Now, let's calculate 7^3:
7^3 = 7 * 7 * 7 = 343
Therefore, 7^(-3) simplifies to 1 / 343.