Number System: Exponent Test-1

This is an assessment test.
To draw maximum benefit, study the concepts for the topic concerned.
Kindly take the tests in this series with a pre-defined schedule.

Number System: Exponent Test-1

Please wait while the activity loads.
If this activity does not load, try refreshing your browser. Also, this page requires javascript. Please visit using a browser with javascript enabled.

If loading fails, click here to try again

Congratulations - you have completed Number System: Exponent Test-1.You scored %%SCORE%% out of %%TOTAL%%.You correct answer percentage: %%PERCENTAGE%% .Your performance has been rated as %%RATING%%

Your answers are highlighted below.

Question 1

(6⁸-6⁷)(6⁹-6⁸)=?

A	36
B	6²
C	25 x 6¹⁵
D	5 x 6¹⁵

Question 1 Explanation:

Using BODMAS and taking out the common powers from the bracket,
we are left with:
6⁷(6-1)6⁸(6-1)
6⁷6⁸(6-1) (6-1)
6¹⁵ x 5 x 5
25 x 6¹⁵

Question 2

What is the value of x if 8^10x-4= 64^2x+4

A	1
B	2
C	3
D	4

Question 2 Explanation:

Since the bases of the two sides are not equal, we first equate the bases.
We know 8²=64
Therefore,
64^2x+4 = 8 ^{2( 2x+4)} = 8 ^4x+8
Now let’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

What’s the largest value for x, so that 3^x is a factor of 54¹²?

A	6
B	12
C	24
D	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 10⁹?