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Exponents And Powers

Question
CBSEENMA8002730

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