Question

# Simplify and write in exponential form: $\dfrac{{{{\left( {{3^2}} \right)}^3} \times {{\left( { - 2} \right)}^5}}}{{{{\left( { - 2} \right)}^3}}}$

Verified
91.8k+ views
Hint: In the given question, we have been given an expression which needs to be simplified. It can be easily done if we know the formula of division of two numbers with equal base but unequal exponent.
Formula Used:
For this question, we are going to use the formula for division of two numbers with equal base but unequal exponent, which is,
$\dfrac{{{a^m}}}{{{a^n}}} = {a^{m - n}}$

$A = \dfrac{{{{\left( {{3^2}} \right)}^3} \times {{\left( { - 2} \right)}^5}}}{{{{\left( { - 2} \right)}^3}}}$
$A = \dfrac{{{{\left( {{3^2}} \right)}^3} \times {{\left( { - 2} \right)}^5}}}{{{{\left( { - 2} \right)}^3}}} = {\left( {{3^2}} \right)^3} \times {\left( { - 2} \right)^{5 - 3}}$
But, we know, ${\left( {{a^n}} \right)^m} = {a^{m \times n}}$ and ${\left( { - a} \right)^{2m}} = {\left( a \right)^{2m}}$
Hence, $A = {\left( {{3^2}} \right)^3} \times {\left( { - 2} \right)^{5 - 3}} = {\left( 3 \right)^{2 \times 3}} \times {\left( { - 2} \right)^2} = {\left( 3 \right)^6} \times {\left( 2 \right)^2}$
So, $\dfrac{{{{\left( {{3^2}} \right)}^3} \times {{\left( { - 2} \right)}^5}}}{{{{\left( { - 2} \right)}^3}}} = {\left( 3 \right)^6} \times {\left( 2 \right)^2}$
So, the correct answer is “ ${\left( 3 \right)^6} \times {\left( 2 \right)^2}$ ”.