Question

please help me ........​

Answer 1

Answer:

1

Solution:

$\sf \bigg( \dfrac{a^p }{a^q} \bigg)^{p + q} \times \bigg( \dfrac{a^q}{a^r} \bigg)^{q + r} \times \bigg( \dfrac{a^r }{a^p} \bigg)^{r + p}$

$\sf = ( a^{p - q})^{p + q} \times ( a^{q - r})^{q - r} \times ( a^{r - p})^{r + p}$

$\sf = a^{(p - q)(p + q)} \times a^{(q - r)(q - r)} \times a^{(r - p)(r + p)}$

$\sf = a^{p^2 - {q}^{2} } \times a^{ {q}^{2} - {r}^{2} } \times a^{ {r}^{2} - {p}^{2} }$

$\sf = a^{p^2 - {q}^{2} + {q}^{2} - {r}^{2} + {r}^{2} - {p}^{2} }$

$\sf = a^0 = 1$

Laws of exponents used:

• a^m / a^n = a^( m - n )

• ( a^m )^n = a^( mn )

• a^m × a^n = a^( m + n )

• a^0 = 1

Identity used:

• ( x - y )( x + y ) = x² - y²

Answer 2

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