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.
Find the numerical equivalent of 9^9⋅9^−6.
To find the numerical equivalent of 9^9⋅9^(-6), we can simplify the expression by applying the power rule of exponents.
According to the power rule of exponents, when multiplying two exponential expressions with the same base, we add their exponents. Therefore, 9^9⋅9^(-6) can be simplified as 9^(9+(-6)).
7^(-6) is equivalent to 1/7^6, so 9^(-6) can be simplified as 1/9^6.
Combining the exponents, we have 9^(9+(-6)) = 9^3.
Hence, the numerical equivalent of 9^9⋅9^(-6) is 9^3 = 729.
What is the missing exponent in the following equation?
h^450/h^? = h^215(1 point)
To find the missing exponent, we can use the property of division of exponents. When dividing exponential expressions with the same base, we subtract the denominators' exponent from the numerator's exponent.
In this case, we have h^450 divided by h^? equals h^215.
Using the property of division of exponents, we can rewrite the equation as h^(450-?) = h^215.
To find the missing exponent, we need to solve the equation 450 - ? = 215.
Subtracting 215 from both sides of the equation, we get -? = -235.
Dividing both sides by -1, we find that ? = 235.
Therefore, the missing exponent is 235.
Simplify 12^87 ÷ 12^25.
To simplify the expression 12^87 ÷ 12^25, we can use the property of division of exponents. When dividing exponential expressions with the same base, we subtract the exponents.
In this case, we have 12^87 divided by 12^25.
Using the property of division of exponents, we can rewrite the expression as 12^(87-25).
Subtracting the exponents, we have 12^62.
Therefore, 12^87 ÷ 12^25 simplifies to 12^62.
What is the missing number in this simplified exponential expression: 7^? ÷ 7^5 = 7^12?
To determine the missing number, we can simplify the expression by using the property of division of exponents.
The property of division of exponents states that when dividing exponential expressions with the same base, we subtract the exponent in the denominator from the exponent in the numerator.
In this case, we have 7^? ÷ 7^5 = 7^12.
Using the property of division of exponents, we can rewrite the expression as 7^(? - 5) = 7^12.
According to this equation, the exponent ? - 5 must equal 12.
Solving the equation ? - 5 = 12, we can add 5 to both sides:
? - 5 + 5 = 12 + 5
? = 17
Therefore, the missing number in the simplified exponential expression is 17.
What is the value of 6.9−2^0?(1 point)
7.9
4.9
6.9
5.9
The value of 6.9^(-2^0) is equal to 6.9.
What is the value of 6.9 − 2^0?(1 point)
7.9
4.9
6.9
5.9
The value of 6.9 - 2^0 is equal to 6.9 - 1 which is 5.9.
Apply the Zero Power Rule to create an equivalent expression to 9 ⋅ (− 33)^0 + 3/2(8 − 27^0). (2 points)
9 ⋅ (− 33)^0 + 3/2(8 − 27^0) = ___ ⋅ ___ + 3/2 (___ – ___)
Fill in the blanks.
Applying the Zero Power Rule, any non-zero number raised to the power of 0 is equal to 1.
Therefore, (-33)^0 is equal to 1.
Using this information, we can rewrite the expression:
9 ⋅ (-33)^0 + 3/2(8 − 27^0) = 9 ⋅ 1 + 3/2(8 - 1)
So, the equivalent expression is 9 ⋅ 1 + 3/2(8 - 1).
Solve the expression 15 ⋅ 8^0/5 + 4(7^0 − 6). (1 point)
15 ⋅ 8^0/5 + 4(7^0 − 6) =
To solve the expression, we can simplify each term step by step:
15 ⋅ 8^0/5 + 4(7^0 − 6)
Since any non-zero number raised to the power of 0 is equal to 1, we can simplify 8^0 to 1:
15 ⋅ 1/5 + 4(7^0 − 6)
Next, we simplify 7^0 to 1:
15 ⋅ 1/5 + 4(1 − 6)
Now, let's simplify within the parentheses:
15 ⋅ 1/5 + 4(-5)
Now, perform the multiplication and addition:
3 + (-20)
Which simplifies to:
-17
Therefore, the result of the expression 15 ⋅ 8^0/5 + 4(7^0 − 6) is -17.
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3^−17/8^−14 with positive exponents only. (1 point)
3^−17/8^−14 =
To apply the property of negative integer exponents and generate an expression with positive exponents only, we can rewrite the expression as follows:
3^(-17)/8^(-14)
Using the property of negative exponents, we can move the base with the negative exponent to the denominator and change the exponent sign to positive:
1 / (3^17 * 8^14)
Therefore, the equivalent expression with positive exponents only is 1 / (3^17 * 8^14).
Apply the Properties of Integer Exponents to generate equivalent expressions to (7^−3)^7 ⋅ 7^20/6^−2 with only positive exponents, then solve the expression. Provide the answer as an improper fraction. (1 point)
(7^−3)^7 ⋅ 7^20/6^−2 =
To generate equivalent expressions with only positive exponents, we can apply the properties of integer exponents.
First, we apply the property of raising a power to a power: (a^m)^n = a^(m*n).
(7^(-3))^7 equals 7^(-3*7) which simplifies to 7^(-21).
Next, we apply the property of division of exponents: a^m / a^n = a^(m - n).
7^20 / 6^(-2) equals 7^20 * 6^2.
Now, we can combine the simplified exponents by multiplying them: 7^(-21) * 7^20 * 6^2.
Using the property of multiplication of exponents, 7^(-21) * 7^20 equals 7^(20 - 21) which simplifies to 7^(-1).
The final expression is 7^(-1) * 6^2.
Now, we apply the property of negative exponent: a^(-n) = 1 / a^n.
Therefore, the expression becomes 1/7^1 * 6^2 = 1/7 * 6^2 = 36/7.
Therefore, the solution to the expression (7^−3)^7 ⋅ 7^20/6^−2 is 36/7 as an improper fraction.
Apply the product rule of integer exponents to find the numerical equivalent of 12^−5 ⋅ 12^7. Show your work and explain how you used the product rule of integer exponents.
The product rule of integer exponents states that when multiplying exponential expressions with the same base, we add the exponents.
Using this rule, we can find the numerical equivalent of 12^(-5) ⋅ 12^7 as follows:
12^(-5) ⋅ 12^7 = 12^(-5+7)
We can simplify the exponents inside the parentheses:
12^(-5+7) = 12^2
Therefore, the numerical equivalent of 12^(-5) ⋅ 12^7 is 12^2.
To find the value of 12^2, we can calculate:
12^2 = 12 * 12 = 144
Hence, the final numerical equivalent is 144.
Do convection currents of thermal energy form in Earth’s crust? Why or why not?
Yes, convection currents of thermal energy do form in Earth's crust.
The Earth's crust is not a solid, rigid layer but rather composed of tectonic plates that are constantly moving. Heat is generated within the Earth's mantle through internal processes such as radioactive decay. This heat energy is transferred to the crust through conduction.
As the mantle receives heat energy, it becomes less dense and rises towards the surface. As it reaches the surface, it cools down, becomes denser, and starts to sink back into the mantle. This cyclic motion of warm material rising and cool material sinking creates convection currents of thermal energy within the Earth's crust.
These convection currents in the crust play a crucial role in plate tectonics, which is the theory that explains the movement of the Earth's lithospheric plates. The convection currents in the mantle drive the movement of the tectonic plates on the Earth's surface, causing processes such as continental drift, volcanic activity, and the formation of mountain ranges.
Therefore, convection currents of thermal energy do occur in Earth's crust as a result of heat transfer and the movement of tectonic plates.