The equivalent expression to 5^9 * 5^-13 with only positive exponents, generated by applying the properties of integer exponents, is:
A. 1/5^4
A. 1/5^4
B. 5^9/5^-13
C. 5^4
D. 1/625
A. 1/5^4
A. the Property of Negative Exponents and the Product Rule of Exponents
B. only the Property of Negative Exponents
C. only the Power Rule of Exponents
D. only the Product Rule of Exponents
A. The Property of Negative Exponents and the Product Rule of Exponents.
(−4)^3/7^2
7^2/(−4)^3
1/7^2 ⋅ (−4)^−3
4^3/7^2
1/7^(2) ⋅ (−4)^(3)
Therefore, the correct option is:
C. 1/7^2 â‹… (-4)^-3
1⋅4^−3
64
60/4^−3
1/64
(15^(-3) â‹… 47)^(0) = 1
Therefore, the correct option is:
1
The expression (15^(-3) â‹… 47)^(0^4-3) simplifies as follows:
(15^(-3) â‹… 47)^(0^4-3) = (15^(-3) â‹… 47)^1 = 15^(-3) â‹… 47
Therefore, the equivalent expression, generated by applying the Properties of Integer Exponents, is:
15^(-3) â‹… 47
1⋅4^−3
64
60/4^−3
1/64
(15^(-3) â‹… 4^7)^0/4^(-3) = 1/4^(-3)
Applying the property of negative exponents, we know that 4^(-3) is equivalent to 1/4^3.
Therefore, the equivalent expression, generated by applying the Properties of Integer Exponents, is:
1/4^3
This simplifies further to:
1/64
So, the correct option is:
D. 1/64
2^12⋅9^−12/2^9⋅9^−10
2^3/9^2
2^−7⋅9^−1/2^9⋅9^−10
2^3â‹…9^2
(2^(-3)â‹…9^3)^(-4)/2^9â‹…9^(-10)
= (2^(-3)â‹…(3^2)^3)^(-4)/2^9â‹…9^(-10)
= (2^(-3)â‹…3^(2â‹…3))^(-4)/2^9â‹…9^(-10)
= (2^(-3)â‹…3^6)^(-4)/2^9â‹…9^(-10)
= (2^(-3â‹…4)â‹…3^(6â‹…-4))/2^9â‹…9^(-10)
= (2^(-12)â‹…3^(-24))/2^9â‹…9^(-10)
= 2^(-12+9)â‹…3^(-24+10)
= 2^(-3)â‹…3^(-14)
= 1/2^3â‹…1/3^14
= 1/8â‹…1/4782969
= 1/38263752
Therefore, the equivalent expression to (2^(-3)â‹…9^3)^(-4)/2^9â‹…9^(-10) with only positive exponents is:
1/38263752
So the correct option is not provided in the given list.
2^12 ⋅ 9^−12/2^9 ⋅ 9^−10
2^3/9^2
2^−7 ⋅ 9^−1/2^9 ⋅ 9^−10
2^3 â‹… 9^2
First, we can rewrite (2^(-3)â‹…9^3)^(-4) as (2^(-3*(-4))â‹…9^(3*(-4))) = 2^12â‹…9^(-12).
Next, we rewrite 2^9â‹…9^(-10) as 2^9â‹…9^(-10) = 2^3â‹…9^2.
So, the expression becomes (2^12â‹…9^(-12))/(2^3â‹…9^2).
Now, we can apply the quotient rule of exponents, which states that (a^m)/(a^n) = a^(m-n), to rewrite the expression as 2^(12-3)â‹…9^(-12-2) = 2^9â‹…9^(-14).
Thus, the correct option that represents the equivalent expression, generated by applying the Properties of Integer Exponents, is:
A. 2^12 â‹… 9^(-12)/2^9 â‹… 9^(-10)
First, let's simplify (2^(-3)â‹…9^3)^(-4) as (2^(-3*(-4))â‹…9^(3*(-4))) = 2^12â‹…9^(-12).
Next, the expression becomes (2^12â‹…9^(-12))/2^9â‹…9^(-10).
Using the quotient rule, we can simplify this expression further:
= 2^(12-9)â‹…9^(-12+10)
= 2^3â‹…9^(-2)
= 8/9^2
= 8/81
Therefore, the correct option that represents the equivalent expression is:
C. 8/81
French Troops in the French and Indian War:
1. Guerilla Warfare: The French employed guerilla warfare tactics, using ambushes and hit-and-run tactics against British forces.
2. Fortifications: French troops built fortified positions, such as Fort Duquesne, to protect their territories.
3. Native American Allies: The French actively formed alliances with various Native American tribes in order to gain their support and assistance in combat.
American Patriots during the Revolution:
1. Asymmetric Warfare: The American patriots utilized asymmetric warfare tactics, avoiding direct confrontations with British regulars and instead focusing on hit-and-run tactics and harassing the enemy.
2. Militia and Guerrilla Tactics: Patriot forces consisted of local militias that were familiar with the terrain, allowing them to launch surprise attacks and disappear quickly.
3. Skirmishes and Ambushes: The patriots engaged in numerous skirmishes and ambushes, targeting British supply lines and isolated units.
4. Fabian Strategy: American military leaders like George Washington adopted a Fabian strategy, avoiding decisive battles and instead prolonging the war, wearing down the British forces over time.
While both the French troops and American patriots employed tactics that emphasized mobility and unconventional warfare, the specific context and objectives of each conflict led to some differences in their approach. The French focused on defending their territories and utilizing Native American alliances, whereas the American patriots aimed to wear down the British and gain independence through a combination of guerrilla tactics and defensive strategies.
1. Guerilla Warfare: Both the French troops and American patriots utilized guerilla warfare tactics. This involved ambushing enemy forces, launching surprise attacks, and then quickly retreating to minimize casualties and maximize the element of surprise.
2. Hit-and-Run Attacks: Both the French and American forces frequently engaged in hit-and-run attacks. They would strike the enemy and then withdraw rapidly before the opposing force could mount a counterattack, taking advantage of their knowledge of the local terrain to swiftly disappear.
3. Utilizing Irregular Forces: Both sides made effective use of irregular forces. The French employed Native American allies during the French and Indian War, while the American patriots relied on local militias during the Revolution. These irregular forces were essential for conducting small-scale raids, gathering intelligence, and disrupting enemy supply lines.
4. Skirmishes and Ambushes: Both the French and American forces engaged in skirmishes and ambushes as part of their tactical repertoire. This involved targeting vulnerable British or enemy units, supply convoys, or smaller outposts, inflicting damage while avoiding direct confrontations with larger and better-trained regular forces.
It's worth mentioning that while these tactics showcased some similarities, the overall strategies and goals of the French troops and American patriots differ significantly due to factors such as the nature of the conflicts, geographical considerations, and the overall military capabilities of the opposing forces.
3^7⋅3^−9= ?
3^7⋅3^−9 = 3^(7 + (-9))
Simplifying the exponent gives us:
3^(-2)
To convert this into a positive exponent, we can apply the property of negative exponents, which states that a^(-n) = 1 / a^n:
3^(-2) = 1 / 3^2
Simplifying further:
1 / 3^2 = 1 / 9
Therefore, the equivalent expression for 3^7⋅3^−9 with only positive exponents is:
1/9
2^2/2^−4=
2^2/2^(-4) = 2^(2 - (-4))
Simplifying the exponent gives us:
2^(2 + 4) = 2^6
Therefore, the equivalent expression for 2^2/2^(-4) with only positive exponents is:
2^6
Solving the expression, we have:
2^6 = 64
Thus, the solution to the expression 2^2/2^(-4) as a whole number is 64.
4^0 ⋅ 5^−2/(−2^)−3=
First, let's simplify the expression:
4^0 ⋅ 5^(-2)/(−2)^(-3) = 1 ⋅ 5^(-2)/(−2)^(-3)
Now, let's utilize the property that a^(-n) = 1/a^n to convert the negative exponents into positive exponents:
1 ⋅ 5^(-2)/(−2)^(-3) = 1 ⋅ 5^(-2)/(1/(-2)^3)
Simplifying further:
1 â‹… 5^(-2)/(1/(-8))
Since dividing by a fraction is equal to multiplying by its reciprocal, we can rewrite the expression:
1 â‹… 5^(-2) * (-8/1)
Applying the property that a^(-n) = 1/a^n, we get:
1 * (1/5^2) * (-8/1)
Simplifying:
1 * 1/25 * (-8)
Finally, evaluating the product gives us:
-8/25
Therefore, the equivalent expression for 4^0 ⋅ 5^(-2)/(−2)^(-3) with only positive exponents is:
-8/25
(14^3⋅27^−7)^0/3^4=?
First, let's simplify the expression:
(14^3â‹…27^(-7))^0/3^4
The property of any number raised to the power of zero is equal to 1. Therefore,
(14^3â‹…27^(-7))^0 = 1
The expression now simplifies to:
1/3^4
Since 3^4 equals 81, the answer is:
1/81
Therefore, the equivalent expression for (14^3â‹…27^(-7))^0/3^4 with only positive exponents is:
1/81
(4^3 ⋅ 7^−2)^−5/7^9 ⋅ 4^−13= ?
(4^3 ⋅ 7^−2)^−5/7^9 ⋅ 4^−13= ?
(4^3 ⋅ 7^−2)^−5/7^9 ⋅ 4^−13=
(4^3 ⋅ 7^−2)^−5/7^9 ⋅ 4^−13=