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## Number System: Exponent Test-1

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Question 1 |

(6

^{8}-6^{7})(6^{9}-6^{8})=?36 | |

6 ^{2} | |

25 x 6 ^{15} | |

5 x 6 ^{15} |

Question 1 Explanation:

Using BODMAS and taking out the common powers from the bracket,

we are left with:

6

6

6

25 x 6

we are left with:

6

^{7}(6-1)6^{8}(6-1)6

^{7}6^{8}(6-1) (6-1)6

^{15}x 5 x 525 x 6

^{15}Question 2 |

What is the value of x if 8

^{10x-4 }= 64^{2x+4}1 | |

2 | |

3 | |

4 |

Question 2 Explanation:

Since the bases of the two sides are not equal, we first equate the bases.

We knowÂ 8

Therefore,

64

Now letâ€™s change our original equation:

8

8

Thus, 10x -4 = 4x + 8

6x = 12

x = 2

We knowÂ 8

^{2}=64Therefore,

64

^{2x+4}Â =Â Â 8^{2( 2x+4)}=Â Â 8^{4x+8}Now letâ€™s change our original equation:

8

^{10x-4}= 64^{2x+4}8

^{10x-4}= 8^{4x+8}Thus, 10x -4 = 4x + 8

6x = 12

x = 2

Question 3 |

Whatâ€™s the largest value for x, so that 3

^{x}is a factor ofÂ 54^{12}?6 | |

12 | |

24 | |

36 |

Question 3 Explanation:

$ \begin{array}{l}Let\,us\,reduce\,the\,number\,{{54}^{{12}}}\operatorname{int}o\,\,factors\,\,of\,\,3\\{{54}^{{12}}}={{(2\times 27)}^{{12}}}\\={{(2\times 9\times 3)}^{{12}}}\\=\,\,{{(2\times 3\times 3\times 3)}^{{12}}}\\=\,\,({{2}^{{12}}}{{3}^{{12}}}{{3}^{{12}}}{{3}^{{12}}})\\=\,\,{{2}^{{12}}}{{3}^{{36}}}\end{array}$

Question 4 |

What is the value of 6.12 x 10

^{9}? 0.00000000612 | |

0.000000612 | |

6.12 | |

6120000000 |

Question 4 Explanation:

This is a simple problem.

The number effectively becomes 612 x 10

. All you need to do is place seven zeros after the two.

The number effectively becomes 612 x 10

^{7}. All you need to do is place seven zeros after the two.

Question 5 |

12

^{8}14^{6}22^{5}/2^{25}3^{7}7^{6}11^{5}= ?2 | |

3 | |

6 | |

12 |

Question 5 Explanation:

The numerator reduces to:

2

Dividing by

2

we obtain 2

2

^{27}3^{8}7^{6}11^{5}Dividing by

2

^{25}3^{7}7^{6}11^{5},we obtain 2

^{2}3^{1}, thus the correct answer is option D.
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