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Exponents and Powers

Short Answer Type

11.

Simplify and express the result in power notation with positive exponent.

$left parenthesis 3 to the power of negative 7 end exponent space divided by space 3 to the power of negative 10 end exponent right parenthesis space cross times space 3 to the power of negative 5 end exponent$

187 Views

12.

Simplify and express the result in power notation with positive exponent.

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102 Views

13.

Find the value of:

$space left parenthesis 3 to the power of 0 plus 4 to the power of negative 1 end exponent right parenthesis space cross times space 2 squared$

121 Views

14.

Find the value of:

$left parenthesis 2 to the power of negative 1 end exponent space cross times space 4 to the power of negative 1 end exponent right parenthesis space divided by space 2 to the power of negative 2 end exponent$

84 Views

15.

Find the value of:

$space open parentheses 1 half close parentheses to the power of negative 2 end exponent space plus space open parentheses 1 third close parentheses to the power of negative 2 end exponent space plus space open parentheses 1 fourth close parentheses to the power of negative 2 end exponent$

100 Views

16.

Find the value of:

$left parenthesis 3 to the power of negative 1 end exponent space plus space 4 to the power of negative 1 end exponent space plus space 5 to the power of negative 1 end exponent right parenthesis to the power of 0$

148 Views

17.

Find the value of:
$space space open curly brackets open parentheses fraction numerator negative 2 over denominator 3 end fraction close parentheses to the power of negative 2 end exponent close curly brackets squared$

78 Views

18.

Evaluate:

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92 Views

19.

Evaluate:

$left parenthesis 5 to the power of negative 1 end exponent space cross times space 2 to the power of negative 1 end exponent space right parenthesis space cross times space 6 to the power of negative 1 end exponent$

76 Views

20.
Find the value of m for which $5 to the power of straight m space divided by space 5 to the power of negative 3 end exponent space equals space 5 to the power of 5.$

∵ $straight a to the power of straight m space divided by space straight a to the power of straight n space equals space straight a to the power of straight m minus straight n end exponent$

∴     L.H.S = $5 to the power of straight m space divided by space 5 to the power of negative 3 end exponent$

             = $5 to the power of straight m minus left parenthesis negative 3 right parenthesis end exponent space equals space 5 to the power of straight m plus 3 end exponent$

Now,     $5 to the power of straight m plus 3 end exponent space equals space 5 to the power of 5$

   Since, bases 5 are equal, therefore exponents are also equal.

i.e.         m + 3 = 5

or                      m = 5 -3 = 2

Thus, the required value of m is 2.