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1. (132)^{7} × (132)^{?} = (132)^{11.5}. | |

A. 3 | B. 4.5 |

C. 4 | D. 3.5 |

Discuss |

answer with explanation

Answer: Option B

Explanation:

$a^m.a^n = a^{m+n}$

(132)^{7} × (132)^{x} = (132)^{11.5}

=> 7 + x = 11.5

=> x = 11.5 - 7 = 4.5

2. $\left(\dfrac{a}{b}\right)^{x-2} = \left(\dfrac{b}{a}\right)^{x-7}.\text{ What is the value of x ?}$ | |

A. 4.5 | B. 4 |

C. 3.5 | D. 3 |

Discuss |

answer with explanation

Answer: Option A

Explanation:

$a^{n} = \dfrac{1}{a^{-n}}$

$\begin{align}&\left(\dfrac{a}{b}\right)^{x-2} = \left(\dfrac{b}{a}\right)^{x-7}\\\\

&\Rightarrow \left(\dfrac{a}{b}\right)^{x-2} = \left(\dfrac{a}{b}\right)^{-(x-7)}\\\\

&\Rightarrow x - 2 = -(x - 7)\\\\

&\Rightarrow x - 2 = -x + 7\\\\

&\Rightarrow x-2 = -x + 7\\\\

&\Rightarrow 2x = 9\\\\

&\Rightarrow x = \dfrac{9}{2} = 4.5

\end{align} $

3. If 7^{(x - y)} = 343 and 7^{(x + y)} = 16807, what is the value of x? | |

A. 3 | B. 1 |

C. 2 | D. 4 |

Discuss |

answer with explanation

Answer: Option D

Explanation:

7^{(x - y)} = 343 = 7^{3}

=> x - y = 3 ---------------------------(Equation 1)

7^{(x + y)} = 16807 = 7^{5}

=> x + y = 5 ---------------------------(Equation 2)

(Equation 1)+ (Equation 2) => 2x = 3 + 5 = 8

=> x = ^{8}⁄_{2} = 4

4. (0.04)^{-2.5} = ? | |

A. 125 | B. 25 |

C. 3125 | D. 625 |

Discuss |

answer with explanation

Answer: Option C

Explanation:

$a^{-n} = \dfrac{1}{a^n}$

$\begin{align}&(0.04)^{-2.5} = \left(\dfrac{1}{.04}\right)^{2.5} = \left(\dfrac{100}{4}\right)^{2.5}

= \left(25\right)^{2.5} = \left(5^2\right)^{2.5}\\\\

&= \left(5^2\right)^{\left(\dfrac{5}{2}\right)}= 5^5 = 3125\end{align}$

5. (6)^{6.5} × (36)^{4.5} ÷ (216)^{4.5} = (6)^{?} | |

A. 2 | B. 4 |

C. 1 | D. 6 |

Discuss |

answer with explanation

Answer: Option A

Explanation:

(6)^{6.5} × (36)^{4.5} ÷ (216)^{4.5}

= (6)^{6.5} × [(6)^{2}]^{4.5} ÷ [(6)^{3}]^{4.5}

= (6)^{6.5} × (6)^{9} ÷ (6)^{13.5}

= (6)^{(6.5 + 9 - 13.5)}

= (6)^{2}

Harpreet

2015-02-14 09:59:31

Good One !! More chapters like Ratio & Proportions , Sequence & Series and some statistics topics like Central tendency, Dispersion , Correlation & regression should be added.

pooja

2014-03-10 18:35:52

it's very nice method each que.each farmula are used

so that's very good simplification thank you very much..........

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