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Exponents and Powers

Short Answer Type

11.
Simplify and express the result in power notation with positive exponent.

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

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

∵ $straight a to the power of straight m space plus space straight a to the power of straight n space equals space straight a to the power of straight m minus straight n end exponent$ and $straight a to the power of straight m space cross times space straight a to the power of straight n space equals space straight a to the power of straight m plus straight n end exponent$

∴ $left parenthesis 3 to the power of negative 7 end exponent space divided by space 3 to the power of negative 10 end exponent right parenthesis space cross times space 3 to the power of negative 5 end exponent space equals space open square brackets 3 to the power of negative 7 minus left parenthesis negative 10 right parenthesis end exponent close square brackets space cross times space 3 to the power of negative 5 end exponent$

                                 = $open square brackets 3 to the power of negative 7 plus 10 end exponent close square brackets cross times 3 to the power of negative 5 end exponent$

                                 = $3 cubed cross times 3 to the power of negative 5 end exponent$

                                 = $3 to the power of 3 plus left parenthesis negative 5 right parenthesis end exponent$

                                 = $3 to the power of negative 2 end exponent equals fraction numerator 1 over denominator left parenthesis 3 right parenthesis squared end fraction$

187 Views

12.

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

$<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

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:

$<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

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 $5 to the power of straight m space divided by space 5 to the power of negative 3 end exponent space equals space 5 to the power of 5.$

87 Views

Previous Year Papers

Test Series

Test Yourself

Short Answer Type

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

11.
Simplify and express the result in power notation with positive exponent.

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