Page 96 - Algebra

Explanation:
1. √5𝑛 = 3125
√5𝑛 = 55 𝑛 or52 =55
In exponents, when bases are the same, power can be equated. 𝑛=5
2
n = 10
2. 0.15÷p2 =15
0.15 = p2 15
p2= 0.01 p = 0.1
3. Speed of the meteoroid = 76 miles per day Time travelled by the meteoroid = 72 days Distance = Speed × Time
Distance = 76 × 72 = 76+2 = 78 miles
4. Using (ab)n = an bn
3x 3 x
3 =3.3 =27×4=108
4x 4 x
3 =3.3 =81×4=324
Therefore,3x +33x +34x =4+108+324=436
5. = 𝑥3(−𝑦)−2𝑎4
𝑦6(−𝑥)−5𝑎−2
Solve using law of exponents = 𝑥3(−𝑥)5𝑎4𝑎2
𝑦6 (−𝑦)2
Using law of exponents
−𝑥8𝑎6 𝑥8𝑎6 𝑥8
= 8 = 8 or 8 −6 −𝑦 𝑦 𝑦𝑎
Compare it with
So, b = 8
c=8
d= – 6
= 2b + c – d
= 16 + 8 – (–6) = 24 + 6
= 30
𝑥𝑏 , 𝑦𝑐𝑎𝑑
Page 95 of 177
Algebra I & II