Question

Answer in step by step please ​

Answer 1

Answer:

(a) m²⁰/n¹⁵

(b) 1/q⁵

(c) y²/3x

Step-by-step explanation:

$(a) \: ( {m}^{ - 4} {n}^{3} {)}^{ - 5} \\ = {m}^{ - 4 \times - 5} \times {n}^{3 \times - 5} \\ = {m}^{20} {n}^{ - 15} = \frac{ {m}^{20} }{ {n}^{15} }$

$(b) \: ( {p}^{6} {q}^{ - 2} )( {p}^{ - 6} {q}^{ - 3} ) \\ = {p}^{6} \times {p}^{ - 6} \times {q}^{ - 2} \times {q}^{ - 3} \\ = {p}^{6 - 6} \times {q}^{ - 2 - 3} \\ = {p}^{0} \times {q}^{ - 5} = \frac{1}{ {q}^{5} }$

$(c) \: \frac{5 {x}^{ - 4} {y}^{8} }{15 {x}^{ - 3} {y}^{6}} \\ = \frac{ {y}^{8} \times {y}^{ - 6} }{3 \times {x}^{ - 3} \times {x}^{4} } \\ = \frac{ {y}^{8 - 6} }{3 \times {x}^{ - 3 + 4} }$

$= \frac{ {y}^{2} }{3 {x}^{1} } \: or \: \frac{ {y}^{2} }{3x }$

Note that here exponential laws are used.

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