Answer:
972 x^16 y^24
Step-by-step explanation:
Simplify the following:
(-2 x^3 y^7)^2 (3 x^2 y^2)^5
Multiply each exponent in -2 x^3 y^7 by 2:
(-2)^2 x^(2×3) y^(2×7) (3 x^2 y^2)^5
2×7 = 14:
(-2)^2 x^(2×3) y^14 (3 x^2 y^2)^5
2×3 = 6:
(-2)^2 x^6 y^14 (3 x^2 y^2)^5
(-2)^2 = 4:
4 x^6 y^14 (3 x^2 y^2)^5
Multiply each exponent in 3 x^2 y^2 by 5:
4 x^6 y^14×3^5 x^(5×2) y^(5×2)
5×2 = 10:
4×3^5 x^6 y^14 x^(5×2) y^10
5×2 = 10:
4×3^5 x^6 y^14 x^10 y^10
3^5 = 3×3^4 = 3 (3^2)^2:
4×3 (3^2)^2 x^6 y^14 x^10 y^10
3^2 = 9:
4×3×9^2 x^6 y^14 x^10 y^10
9^2 = 81:
4×3×81 x^6 y^14 x^10 y^10
3×81 = 243:
4×243 x^6 y^14 x^10 y^10
4 x^6 y^14×243 x^10 y^10 = 4 x^(6 + 10) y^(14 + 10)×243:
4×243 x^(6 + 10) y^(14 + 10)
14 + 10 = 24:
4×243 x^(6 + 10) y^24
6 + 10 = 16:
4×243 x^16 y^24
4×243 = 972:
Answer: 972 x^16 y^24
To divide exponents they have to have the same base and then you just subtract the bottom exponent from the top exponent.
7) k × 3^9
----------- =
3^5
k × 3^9-5 =
k × 3^4 =
k × 81 = 81k
8) x^4 × y^10 × 2^11
------------------------ =
y^8 × 2^7
x^4 × y^10-8 × 2^11-7 =
x^4 × y^2 × 2^4 =
x^4 × y^2 × 16=
16x^4y^2
Answer: True
Step-by-step explanation:
This is true because for a square, all angles and sides are equal. That is no side has a longer length than the other. The diagonals of a square are therefore perpendicular bisectors of each other.
I hope this is clear, please mark as brainliest answer
Answer:
= 
, so the model car is moving away from the fixed point at a rate of approximately 1.7 feet per second.
Step-by-step explanation:
The functions x and y satisfy (x−20)^2+y^2=25 and differentiating gives 2(x−20)dx/dt+2y dy/dt=0. Substituting the three known values and solving for dy/dt yields dy/dt=−32. Since Z=x^2+y^2−−−−−−√, dZ/dt=(2x ^ dx/dt+2y^dy/dt) / 2x2+y2√. Substituting Since Substituting for x, y,
, and 
gives = ,
The answer to this question is false
