Question

Pls i need help :)))))

Answer 1

The simplified form of algebraic expressions are now shown:

Case 1:
`x^{(5)/(3)}`

Case 2:
`m^{(8)/(5) }`

Case 3:
`y^{(11)/(8) }`

Case 4:
`r^{(4)/(5)}\cdot s^{(27)/(8) }`

Case 5:
`6\cdot b^{(19)/(15)}`

Case 6:
`m^{(2)/(5)}`

Case 7:
`\frac{s^{(2)/(7)}}{r^{(3)/(4)}}`

Case 8:
`x^{(3)/(16) }`

Case 9:
`\frac{n^{(1)/(10) }}{m^{(7)/(9) }}`

Case 10:
`\frac{y^{(2)/(9) }}{x^{(8)/(45)}}`

How to simplify algebraic expressions by power properties

In this problem we need to simplify algebraic expressions by power properties, which are introduced below:

Product of two powers:

`a^m \cdot a^n = a^(m+n)`

Division of two powers:

`(a^m)/(a^n) = a^(m - n)`

Power of a power:

`(a^m)^n = a^(m\cdot n)`

Further power properties:

`a^(0) = 1`

Now we proceed to simplify each expression by means of power properties:

Case 1:

`x^{(1)/(3)}\cdot x^{(4)/(3)}`

`x^{(1)/(3) + (4)/(3)}`

`x^{(5)/(3)}`

Case 2:

`m^{(2)/(5)}\cdot (m^(3)/(5))^2`

`m^{(2)/(5)}\cdot m^{(6)/(5)}`

`m^{(2)/(5) + (6)/(5) }`

`m^{(8)/(5) }`

Case 3:

`y^{(3)/(4) }\cdot y^{(5)/(8) }`

`y^{(3)/(4) + (5)/(8) }`

`y^{(6)/(8) + (5)/(8) }`

`y^{(11)/(8) }`

Case 4:

`(r^{(1)/(5) }\cdot s^{(7)/(8)})\cdot (r^{(3)/(5)}\cdot s^{(5)/(2)})`

`(r^{(1)/(5)}\cdot r^{(3)/(5)})\cdot (s^{(7)/(8)}\cdot s^{(5)/(2)})`

`(r^{(1+3)/(5) })\cdot (s^{(14 + 40)/(16) })`

`r^{(4)/(5)}\cdot s^{(27)/(8) }`

Case 5:

`(2\cdot b^{(3)/(5)})\cdot (3\cdot b^{(2)/(3)})`

`6\cdot b^{(3)/(5) + (2)/(3) }`

`6\cdot b^{(9 + 10)/(15) }`

`6\cdot b^{(19)/(15)}`

Case 6:

`\frac{m^{(4)/(5) }}{m^{(2)/(5) }}`

`m^{(4)/(5) - (2)/(5) }`

`m^{(2)/(5)}`

Case 7:

`\frac{s^{(4)/(7)}}{r^{(3)/(4)}\cdot s^{(2)/(7)}}`

`\frac{s^{(4)/(7) - (2)/(7) }}{r^{(3)/(4) }}`

`\frac{s^{(2)/(7)}}{r^{(3)/(4)}}`

Case 8:

`\left(\frac{x^2}{x^{(3)/(2)}} \right)^{(3)/(4)}`

`(x^{2-(3)/(2) })^{(3)/(4) }`

`(x^{(1)/(4) })^{(3)/(4) }`

`x^{(3)/(16) }`

Case 9:

`\frac{m^{(5)/(9) }\cdot n^{(4)/(5) }}{m^{(4)/(3) }\cdot n^{(7)/(10) }}`

`(m^{(5)/(9) - (4)/(3) })\cdot (n^{(4)/(5) -(7)/(10) })`

`m^{-(7 )/(9)}\cdot n^{(1)/(10) }`

`\frac{n^{(1)/(10) }}{m^{(7)/(9) }}`

Case 10:

`\left(\frac{x^{(2)/(5) }\cdot y^{(5)/(6)}}{x^{(2)/(3)}\cdot y^{(1)/(2)}} \right)^{(2)/(3) }`

`(x^{(2)/(5)-(2)/(3) } \cdot y^{(5)/(6)-(1)/(2)})^{(2)/(3) }`

`(x^{-(4)/(15) }\cdot y^{(1)/(3) })^{(2)/(3) }`

`x^{-(8)/(45) }\cdot y^{(2)/(9) }`

`\frac{y^{(2)/(9) }}{x^{(8)/(45)}}`