Select the equivalent expression.\left(\dfrac{3^{-6}}{7^{-3}}\right)^{5}=?( 7 −33 −6 ) 5 =?left parenthesis, start fraction, 3, start superscript, minus, 6, end superscript, divided by, 7, start superscript, minus, 3, end superscript, end fraction, right parenthesis, start superscript, 5, end superscript, equals, question markChoose 1 answer:Choose 1 answer:
Accepted Solution
A:
Answer:[tex]\frac{7^{15}}{3^{30}}[/tex]Step-by-step explanation:The given expression is:[tex](\frac{3^{-6}}{7^{-3}})^{5}[/tex]Moving the expression to the other side in the fraction changes its sign to opposite. A numerator with negative exponent, when written in denominator will have the positive exponent. Using this rule, we can write:[tex](\frac{3^{-6}}{7^{-3}})^{5}\\\\ = (\frac{7^{3}}{3^{6}} )^{5}[/tex]The exponent 5 can be distributed to both numerator and denominator as shown:[tex](\frac{7^{3}}{3^{6}} )^{5}\\\\ = \frac{(7^{3})^{5}}{(3^{6})^{5}}[/tex]The power of a power can be written as a product. i.e.[tex]\frac{(7^{3})^{5}}{(3^{6})^{5}}\\\\ =\frac{7^{15}}{3^{30}}[/tex]So, the expression similar to the given expression and with positive exponents is: [tex]\frac{7^{15}}{3^{30}}[/tex]