Question

1 simplify each expression. write your answer using a negative exponent.

i) $7^{-12} \cdot 7^{5} = $

ii) $10^{-10} \cdot 10^{5} = $

iii) $\frac{3^{4}}{3^{6}} = $

v) $\frac{8^{12}}{8^{13}} = $

Explanation:

Step1: Apply exponent product rule

For $7^{-12} \cdot 7^{5}$, use $a^m \cdot a^n = a^{m+n}$:
$7^{-12 + 5} = 7^{-7}$

Step2: Apply exponent product rule

For $10^{-10} \cdot 10^{5}$, use $a^m \cdot a^n = a^{m+n}$:
$10^{-10 + 5} = 10^{-5}$

Step3: Apply exponent quotient rule

For $\frac{3^4}{3^6}$, use $\frac{a^m}{a^n} = a^{m-n}$:
$3^{4-6} = 3^{-2}$

Step4: Apply exponent quotient rule

For $\frac{8^{12}}{8^{15}}$, use $\frac{a^m}{a^n} = a^{m-n}$:
$8^{12-15} = 8^{-3}$

Answer:

i) $7^{-7}$
ii) $10^{-5}$
iii) $3^{-2}$
v) $8^{-3}$