Question

Simplify: $open square brackets fraction numerator 3 cubed cross times 3 to the power of negative 2 end exponent cross times 3 to the power of 5 over denominator 2 to the power of negative 2 end exponent cross times 2 squared cross times 2 to the power of negative 5 end exponent end fraction close square brackets$

Solution

Since, $straight m to the power of straight a cross times straight m to the power of straight b equals straight m to the power of straight a plus straight b end exponent$

     $space space space space space space therefore space space space space space space space space 3 cubed cross times 3 to the power of negative 2 end exponent cross times 3 to the power of 5 space equals space 3 to the power of 3 plus left parenthesis negative 2 right parenthesis plus 5 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 3 to the power of 8 minus 2 end exponent space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals space 3 to the power of 6$
                    $space space space space space space space space 2 to the power of negative 2 end exponent space cross times space 2 squared space cross times space 2 to the power of negative 5 end exponent space equals space 2 to the power of negative 2 plus 2 minus 5 end exponent$
                                                   = $space space 2 to the power of negative 5 end exponent$
$rightwards double arrow$           $fraction numerator 3 cubed cross times 3 to the power of negative 2 end exponent cross times 3 to the power of 5 over denominator 2 to the power of negative 2 end exponent cross times 2 squared cross times 2 to the power of negative 5 end exponent end fraction space equals space 3 to the power of 6 over 2 to the power of negative 5 end exponent$
                                      $equals space 3 to the power of 6 space cross times space 2 to the power of 5$

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Exponents And Powers

Some More Questions From Exponents and Powers Chapter

Find the multiplicative inverse of the following.
(i) 2^–4 (ii) 10^–5 (iii) 7^–2 (iv) 5^–3 (v) 10^–100

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