Question

$find \: p \: so \: that \: ( {5})^{8} \times ( {5})^{7} = ( { - 5})^{3p}$
​

Answer 1

Given,

${(5)^8(5)^7 = (-5)^{3p}}$

==> ${(5)^{8+7} = (-5)^{3p}}$

==> ${(5)^{15} = (-5)^{3p}}$

==> ${(5)^{15} = (-1 * 5)^{3p}}$

==> ${(5)^{15} = (-1^{3p} * 5^{3p}}$

==> ${{(5)^{15}}^{2} = {(-1^{3p} * 5^{3p)}}}^{2}$

(Squaring on both sides)

==> ${(5)^{30} = (5)^{6p}}$

==> 30 = 6p
( Since, bases are equal , powers are also equal)

==> ${\boxed{p\:=\:6}}$

Answer 2

Answer:

Since, bases are equal , powers are also equal)

==> {\boxed{p\:=\:6}}

p=6