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## Number System: Exponent Test-2

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Question 1 |

0.9

^{6}/(0.3)^{-3}= ?3/(15)9 | |

0.000009/0.003 | |

3 ^{15}/10^{9} | |

9.009/0.333 |

Question 1 Explanation:

0.9

= (0.9)

= (9

= (3

= (3

= (3

^{6}/(0.3)^{-3 }= (0.9)

^{6}(0.3)^{3}= (9

^{6}/10^{6}) x (3^{3}/10^{3})= (3

^{(2)6}/10^{6}) x (3^{3}/10^{3})= (3

^{12}/10^{6}) x (3^{3}/10^{3})= (3

^{15}/10^{9})Question 2 |

If 3

^{4}= 9^{x}, then x = ?.2 | |

4 | |

.6 | |

8 |

Question 2 Explanation:

3

3

2x = 4

x =2

^{4}= 9^{x}3

^{4}= 3^{2x}2x = 4

x =2

Question 3 |

If 9

^{x}/(3^{2}+3^{2}+3^{2})=1/81, then what is the value of x?-2 | |

-3 | |

-4 | |

5 |

Question 3 Explanation:

9

3

3

3

3

^{x}/(3^{x}+3^{x}+3^{x})=1/813

^{2x}/(3^{x}+3^{x}+3^{x})=1/813

^{2x}/3^{x}(3)=1/813

^{2x}/3^{x}(3)=1/813

^{x}/(3)=1/81 so x = -3Question 4 |

If p = 729

^{–4/3}x 324^{3/2}x 8^{1/3}, then what will be the value of p^{1/2}?4/3 | |

9/4 | |

16/81 | |

3/2 |

Question 4 Explanation:

p=729

p=9

p= 9

p= 16/9

p

that is, option a

^{–4/3}x 324^{3/2}x 8^{1/3}p=9

^{3(–4/3)}x 18^{2(3/2)}x 2p= 9

^{–4}x 18^{3}x 2p= 16/9

p

^{1/2}=4/3that is, option a

Question 5 |

If (64)

^{1/2m}= 2^{2m}then what will be the value of m +3/4 | |

–1/4 | |

0 | |

$ \sqrt{\frac{3}{2}}$ |

Question 5 Explanation:

(64)

(8

(8

(8 )

(2

3/m = 2m

2m

m

m = $ \sqrt{\frac{3}{2}}$

^{1/2m}= 2^{2m}(8

^{2})^{1/2m}= 2^{2m}(8

^{2})^{1/2m}= 2^{2m}(8 )

^{1/m}= 2^{2m}(2

^{3})^{1/m}= 2^{2m}3/m = 2m

2m

^{2}= 3m

^{2}= 3/2m = $ \sqrt{\frac{3}{2}}$

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