Question

Directions:Simplify the following monomials.SHOW ALL STEPS!

Answer 1

Answer:

13.Ans;

$\frac{( - 2 {m}^{4} )^{2} }{8 {m}^{2} } = \frac{ {( - 2)}^{2} {m}^{4 \times 2} }{8 {m}^{2} } \\ \\ = \frac{4 {m}^{8} }{8 {m}^{2} } = \frac{4 {m}^{2} ( {m}^{6}) }{4 {m}^{2}(2) } = \frac{ {m}^{6} }{2}$

___o____o___

14.Ans;

$\frac{(2 {a}^{3} {b}^{4} ) ^{3} }{(2a {b}^{2}) ^{5} } = \frac{ {(2)}^{3} {a}^{3 \times 3} {b}^{4 \times 3} }{ {(2)}^{5} {a}^{5} {b}^{2 \times 5} } \\ \\ \\ = \frac{8 {a}^{9} {b}^{12} }{32 {a}^{5} {b}^{10} } = \frac{8 {a}^{5} {b}^{10}( {a}^{4} {b}^{2}) }{8 {a}^{5} {b}^{10} (4) } \\ \\ = \frac{ {a}^{4} {b}^{2} }{4}$

___o___o___

15.Ans;

$\frac{ {(3 {x}^{5} {y}^{3} )}^{5} }{ {(6 {x}^{10} {y}^{7} )}^{2} } = \frac{ {(3)}^{5} {x}^{5 \times 5} {y}^{3 \times 5} }{ {(6)}^{2} {x}^{10 \times 2} {y}^{7 \times 2} } \\ \\ = \frac{243 {x}^{25} {y}^{15} }{36 {x}^{20} {y}^{14} } = \frac{9 {x}^{20} {y}^{14}(27 {x}^{5}y) }{9 {x}^{20} {y}^{14}(4) } \\ \\ \\ = \frac{27 {x}^{5}y }{4}$

___o____o____

16.Ans;

${( \frac{4 {x}^{7} }{6x}) }^{2} = \frac{ {(4 {x}^{7} )}^{2} }{ {(6x)}^{2} } = \frac{ {(4)}^{2} {x}^{7 \times 2} }{ {(6)}^{2} {x}^{2} } \\ \\ \\ = \frac{16 {x}^{14} }{36 {x}^{2} } = \frac{4 {x}^{2}(4 {x}^{12}) }{4 {x}^{2} (9)} = \frac{4 {x}^{12} }{9}$

___o____o___

17.Ans;

$( \frac{2 {y}^{5} }{3 {y}^{2} } )^{2} = \frac{ {(2)}^{2} {y}^{5 \times 2} }{ {(3)}^{2} {y}^{2 \times 2} } = \frac{4 {y}^{10} }{9 {y}^{4} } \\ \\ \\ = \frac{ {y}^{4} (4 {y}^{6}) }{ {y}^{4} (9)} = \frac{4 {y}^{6} }{9}$

___o___o____

18.Ans;

$(\frac{5 {x}^{6} {y}^{2} }{10 {x}^{4} y} ) ^{2} = \frac{ {(5 {x}^{6} {y}^{2} )}^{2} }{ {(10 {x}^{4}y) }^{2} } = \frac{ {(5)}^{2} {x}^{6 \times 2} {y}^{2 \times 2} }{ {(10)}^{2} {x}^{4 \times 2} { {y}^{2} }} \\ \\ \\ = \frac{25 {x}^{12} {y}^{4} }{100 {x}^{8} {y}^{2} } = \frac{25 {x}^{8} {y}^{2}( {x}^{4} {y}^{2}) }{25 {x}^{8} {y}^{2} (4)} \\ \\ \\ = \frac{ {x}^{4} {y}^{2} }{4}$

I hope I helped you^_^