Question

help pls i have been stuck for long time

Answer 1

Answer:

Exponent rules

$\textsf{product rule: }a^b \times a^c=a^{(b+c)}$

$\textsf{quotient rule: }a^b \div a^c=a^{(b-c)}$

$\textsf{power rule: }(a^b)^c=a^{(b \times c)}$

a) Use product rule:

$3^2 \times 3^x=3^{(2+x)}$

$\implies 3^{(2+x)}=3^7$

$\implies 2+x=7$

$\implies x = 5$

b) Use quotient rule:

$7^8 \div 7^y=7^{(8-y)}$

$\implies 7^{(8-y)}=7^6$

$\implies 8-y=6$

$\implies y=2$

c)  Use power rule:

$(q^4)^z=q^{(4z)}$

$\implies q^{(4z)}=q^{12}$

$\implies 4z=12$

$\implies z=3$