Answer:
The answers of the questions are given below :
- a) = 4096
- b) = 1.25
- 3) = m²
- 4) = r⁴s³
- 5) = a⁸/b¹²
Step-by-step explanation:
Question. 1
>> 4⁶
- Hence, the answer is 4096.
Question. 2
>> (2⁶/5³)^-⅓
![\begin{gathered} \qquad\implies{\bigg(\frac{2^6}{5^3}\bigg)^{ - \frac{1}{3}}}\\ \\ \qquad\implies{\bigg(\frac{64}{125}\bigg)^{ - \frac{1}{3}}}\\ \\\qquad\implies{\bigg( \frac{1}{\frac{64}{125}}\bigg)^{ \frac{1}{3}}} \\ \\ \qquad\implies{\bigg( 1 \times \frac{125}{64} \bigg)^{ \frac{1}{3}}} \\ \\ \qquad\implies{\bigg( \frac{125}{64} \bigg)^{ \frac{1}{3}}} \\ \\\qquad\implies{\bigg( \sqrt[3]{ \frac{125}{64}}\bigg)} \\ \\ \qquad\implies{\bigg( \dfrac{5}{4} \bigg)} \\ \\ \qquad\implies{\Big( 1.25\Big)}\end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20%5Cqquad%5Cimplies%7B%5Cbigg%28%5Cfrac%7B2%5E6%7D%7B5%5E3%7D%5Cbigg%29%5E%7B%20-%20%5Cfrac%7B1%7D%7B3%7D%7D%7D%5C%5C%20%20%5C%5C%20%5Cqquad%5Cimplies%7B%5Cbigg%28%5Cfrac%7B64%7D%7B125%7D%5Cbigg%29%5E%7B%20-%20%5Cfrac%7B1%7D%7B3%7D%7D%7D%5C%5C%20%20%5C%5C%5Cqquad%5Cimplies%7B%5Cbigg%28%20%5Cfrac%7B1%7D%7B%5Cfrac%7B64%7D%7B125%7D%7D%5Cbigg%29%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%7D%7D%20%5C%5C%20%20%5C%5C%20%5Cqquad%5Cimplies%7B%5Cbigg%28%201%20%5Ctimes%20%20%5Cfrac%7B125%7D%7B64%7D%20%5Cbigg%29%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%7D%7D%20%5C%5C%20%20%5C%5C%20%5Cqquad%5Cimplies%7B%5Cbigg%28%20%5Cfrac%7B125%7D%7B64%7D%20%5Cbigg%29%5E%7B%20%5Cfrac%7B1%7D%7B3%7D%7D%7D%20%5C%5C%20%20%5C%5C%5Cqquad%5Cimplies%7B%5Cbigg%28%20%5Csqrt%5B3%5D%7B%20%5Cfrac%7B125%7D%7B64%7D%7D%5Cbigg%29%7D%20%20%5C%5C%20%20%5C%5C%20%5Cqquad%5Cimplies%7B%5Cbigg%28%20%5Cdfrac%7B5%7D%7B4%7D%20%5Cbigg%29%7D%20%5C%5C%20%20%5C%5C%20%5Cqquad%5Cimplies%7B%5CBig%28%201.25%5CBig%29%7D%5Cend%7Bgathered%7D)
- Hence, the answer is 1.25.
Question. 3
>> (m^2/3)•(m^4/3)
Question. 4
>> (r¹² s⁹)^⅓
- Hence, the answer is r⁴s³.
Question. 5
>> (a⁴/b⁶)^2
- Hence, the answer is a⁸/b¹².
Answer:
1,422.33
Step-by-step explanation:
(a) The inverse of 1234 (mod 4321) is x such that 1234*x ≡ 1 (mod 4321). Apply Euclid's algorithm:
4321 = 1234 * 3 + 619
1234 = 619 * 1 + 615
619 = 615 * 1 + 4
615 = 4 * 153 + 3
4 = 3 * 1 + 1
Now write 1 as a linear combination of 4321 and 1234:
1 = 4 - 3
1 = 4 - (615 - 4 * 153) = 4 * 154 - 615
1 = 619 * 154 - 155 * (1234 - 619) = 619 * 309 - 155 * 1234
1 = (4321 - 1234 * 3) * 309 - 155 * 1234 = 4321 * 309 - 1082 * 1234
Reducing this leaves us with
1 ≡ -1082 * 1234 (mod 4321)
and so the inverse is
-1082 ≡ 3239 (mod 4321)
(b) Both 24140 and 40902 are even, so there GCD can't possibly be 1 and there is no inverse.
Answer:
What is the question?
Step-by-step explanation:
3a+11=7a-13
move 7a to the other side
sign changes from +7a to -7a
3a-7a+11= 7a-7a-13( combine like terms)
3a-7a+11= -13
-4a+11= -13
move 11 to the other side
sign changes from +11 to -11
-4a+11-11= -13-11
-4a= -13-11
-4a= -24
divide both sides by -4 to get a by itself
-4a/-4= -24/-4
Answer: a= 6
