Answer:
Step-by-step explanation:
<h3>#7</h3>
- 5⁵(16²5³)³ = 5⁵(2⁴)³(5³)³ = 5⁵2¹²5⁹ = 5¹⁴2¹²
<h3>#8</h3>
- (8⁴5³/8⁵)² = (5³/8)² = (5³)²/(2³)² = 5⁶ / 2⁶
<h3>#9</h3>
- (5⁸3⁷/5⁴)¹⁰ = (5⁴3⁷)¹⁰ = (5⁴)¹⁰(3⁷)¹⁰ = 5⁴⁰3⁷⁰
<h3>#10</h3>
<u>Multiplying powers with same base:</u>
- Same base with powers added up
<u>Multiplying powers with same exponent but different base:</u>
- Same exponent with bases multiplied
Answer:
1. x + y = 25
2. x - y = 7
3. x = 16, y = 9
Step-by-step explanation:
(x + y = 25) + (x - y = 7)
2x (the y cancels) = 32
32/2 = 16, x = 16
substitute x in either equation
16 + y = 25
y = 9
Answer:
$25.96
Step-by-step explanation:
Answer:
x = -1 and y = 1/2
Step-by-step explanation:
Let u = 1/x, and v = 1/y
Then the pair of equations
-3/x + 4/y = 11
1/x - 2/y = -5
Can be written as
-3u + 4v = 11 .................................(1)
u - 2v = -5......................................(2)
From (2)
u = 2v - 5 .......................................(3)
Substituting (3) into (1)
-3(2v - 5) + 4v = 11
-6v + 15 + 4v = 11
-6v + 4v = 11 - 15
-2v = -4
v = 4/2 = 2
Substituting this value of v in (3)
u = 2v - 5
u = 2(2) - 5
= 4 - 5
= -1
That is
u = -1, v = 2
Since u = 1/x, and v = 1/y, we have
1/x = -1
=> x = -1
And
1/y = 2
=> y = 1/2
Therefore
x = -1 and y = 1/2
