Question

simplify giving answers with positive index​

Answer 1

download photomath app and just scan this problem it will give u correct answer!!

Answer 2

$\Large{\underline{\underline{\huge{\bold{Question \: :-}}}}}$

$\Large\sf\frac{(7 {p}^{2} {q}^{9} {r}^{5})^{2} (4pqr)^{3} }{ (14 {p}^{6} {q}^{10} {r}^{4)^{2} } }$

$\Large{\underline{\underline{\huge{\bold{Solution \: :-}}}}}$

~First we multiply the value of the exponent which is outside the bracket to the exponents of the digits inside the bracket

$\Large\sf \: = \frac{7 {p}^{4} {q}^{18} {r}^{10} \times {4}^{3} {p}^{3} {r}^{3} }{ {14}^{2} {p}^{12} {r}^{8} }$

~Now we write the constants and the variables separately

$\Large\sf \: = \frac{ {7}^{2} \times {4}^{3} }{ {14}^{2} } \times \frac{ {p}^{4 + 3} {q}^{18 \times 3} {r}^{10 + 3} }{ {p}^{12} {r}^{8} }$

~In the next step, we'll multiply and solve

$\Large\sf \: \frac{7 \times 7 \times 4 \times 4 \times 4}{14 \times 14} \times \frac{ {p}^{7} \ {q}^{21} {r}^{13} }{ {p}^{12} {q}^{20} {r}^{8} }$

(To make the equation simpler, we'll write the "14×14" as (7×2)² = 7×7×2×2)

$\Large\sf \: \frac{7 \times 7 \times 4 \times 4 \times 4}{7 \times 7 \times2 \times 2} \times \frac{ {p}^{7} \ {q}^{21} {r}^{13} }{ {p}^{12} {q}^{20} {r}^{8} }$

~Now Cancel and solve!!

$\large\sf\: = 4 \times 4 \: {p}^{7 - 12} \: {q}^{21 - 20} \: {r}^{13 - 8}$

$\Large\sf \underline\color{purple}{16 \: {p}^{ - 5} \: {q}^{1} \: {r}^{5} }$