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## Number System: Exponent Test-3

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Question 1 |

Which of the following expressions is equal to 2

^{18}Â ?(2 ^{3})^{6} | |

2 ^{9+2} | |

2 ^{3}2^{6} | |

9x2 ^{6} |

Question 1 Explanation:

The correct expression in this case is option A.

x

x

^{mn }equals to (x^{m})^{n}Question 2 |

What will be the value of P= 4

^{a}+4^{a}+4^{a}+4^{a}16 ^{a} | |

4 ^{4a} | |

4 ^{a+1} | |

None |

Question 2 Explanation:

= 4

= 4

= 4

= 4

^{a}+4^{a}+4^{a}+4^{a}= 4

^{a}(1+1+1+1)= 4

^{a}x ( 4)= 4

^{a+1}Question 3 |

If q = {y(y

^{2})^{4}} / y^{5}when y is greater than 0 then what would be the exponent of y.2 | |

3 | |

4 | |

5 |

Question 3 Explanation:

Since the question is to find the exponents of y in {y(y

Therefore ={y(y

={y x y

So the exponent of y is 4

^{2})^{4}} / y^{5}Therefore ={y(y

^{2})^{4}} / y^{5}={y x y^{8}} / y^{5}={y x y

^{8}} / y^{5}= { y^{9}} / y^{5}= y^{4}So the exponent of y is 4

Question 4 |

If a and b are not equal to 0, then a

^{18}b^{9 }must bePositive | |

Negative | |

An integer | |

both A or B |

Question 4 Explanation:

If a is negative and b is positive then the result will be positive

If b is negative and a is positive then the result will be negative

So we will consider both the cases and therefore the number can be positive of negative

So the right answer is D

If b is negative and a is positive then the result will be negative

So we will consider both the cases and therefore the number can be positive of negative

So the right answer is D

Question 5 |

If a and b are positive integers and a

^{4}+b^{5}= 259, then value of a + b =?7 | |

9 | |

6 | |

5 |

Question 5 Explanation:

We have a

So from option A = 7 so the value of A and B(1,6)(2,5)(3,4) and vice-versa

but no one option satisfy the condition so option a is rejected

For option B i.e.9 the pairs are (1,8), (2,6), (3,5), (4,4) and vice versa

For option C i.e. for 6 the pairs are (1,5), (2,4), (3,3) and vice versa

For option D i.e. for 5 the pairs are (1,4), (2,3), Â and vice versa

See 2

So the right answer is 5 option D

^{4}+b^{5}= 259So from option A = 7 so the value of A and B(1,6)(2,5)(3,4) and vice-versa

but no one option satisfy the condition so option a is rejected

For option B i.e.9 the pairs are (1,8), (2,6), (3,5), (4,4) and vice versa

For option C i.e. for 6 the pairs are (1,5), (2,4), (3,3) and vice versa

For option D i.e. for 5 the pairs are (1,4), (2,3), Â and vice versa

See 2

^{4}+3^{5}= 259So the right answer is 5 option D

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