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## Number System: Exponent Test-4

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Question 1 |

If 2

^{3x }= 64 and 3^{âˆšy}= 81 then what will be the value of {(3^{x-1})3^{-2}} / 1/3^{y}3/y | |

3 ^{15} | |

45 | |

None |

Question 1 Explanation:

2

2

3x = 6

x = 2

now 3

3

âˆšy = 4

y = 16

Therefore the value of {(3

{3

= 3

^{3xÂ }= 642

^{3xÂ }= 2^{6}3x = 6

x = 2

now 3

^{âˆšy}Â = 813

^{âˆšy}= 3^{4}âˆšy = 4

y = 16

Therefore the value of {(3

^{x-1})3^{-2}} / 1/3^{16}{3

^{1}x 1/9 } / 1/3^{16}= 3

^{15}so option BQuestion 2 |

What will be the value of {a

^{-2}/y^{6 }} x (a^{-4}y^{-6}/z^{3})^{4}a ^{-18 }y^{-30} z^{-12} | |

a ^{-14} y^{-30} z^{-12} | |

a ^{-14} y^{-30} z^{-10} | |

None |

Question 2 Explanation:

= {a

= {a

= {a

= (a

So option A

^{-2}/y^{6 }} x (a^{-4}y^{-6}/z^{3})^{4}= {a

^{-2}y^{-6 }} x (a^{-4}y^{-6}z^{-3})^{4}= {a

^{-2}y^{-6 }} x (a^{-12}y^{-24}z^{-12})= (a

^{-18 }y^{-30 }z^{-12})So option A

Question 3 |

What will be the exponent value of 2 value of {5

^{4}a^{3}/2^{4}b^{0}}^{3}{4^{-3}a^{-2}/5^{3}b}^{-3}18 | |

12 | |

6 | |

none |

Question 3 Explanation:

{5

{4

={5

{4

= {5

={5

= the exponent of 2 from here is 6 So option C is the right answer

^{4}a^{3}/2^{4}b^{0}}^{3}{4

^{-3}a^{-2}/5^{3}b}^{-3}={5

^{4}a^{3}2^{-4}b^{0}}^{3}{4

^{-3}a^{-2}5^{-3}b}^{-3}= {5

^{20}a^{9}2^{-12}b^{0}} {4^{9}a^{6}5^{9}b}={5

^{20}a^{9}2^{-12}b^{0}} {2^{18}a^{6}5^{9}b}= the exponent of 2 from here is 6 So option C is the right answer

Question 4 |

What is the value of x if 4

^{(x +2)}= 1/164 | |

-4 | |

-2 | |

2 |

Question 4 Explanation:

4

4

4

(x +2) = -2

x = -4

^{(x +2)}= 1/164

^{(x +2)}= 1/4^{2}4

^{(x +2)}= 4^{-2}(x +2) = -2

x = -4

Question 5 |

If 3

^{(2x+2)}= 243^{(4x)}then what will be the value of x1/20 | |

1/22 | |

1/18 | |

None |

Question 5 Explanation:

3

3

(2x+2) = 5(4x)

x = 1/9

^{(2x+2)}= 243^{(4x)}3

^{(2x+2)}= 3^{5(4x)}(2x+2) = 5(4x)

x = 1/9

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