Question

What is the value of the expression?

Answer 1

\(\large {
\cfrac{7^{-3}\cdot 7^9}{7^{-8}}\implies \cfrac{7^{-3}\cdot 7^9}{1}\cdot \cfrac{1}{7^{-8}}\implies 7^{-3}\cdot 7^9\cdot 7^{\color{brown}{ +8}}
}\)

Answer 2

Yeah that works too.

Answer 3

recall what Astrophysics said \(\bf a^{{\color{red} n}} \implies \cfrac{1}{a^{-\color{red} n}}
\qquad \qquad

\cfrac{1}{a^{-\color{red} n}}\implies \cfrac{1}{\frac{1}{a^{\color{red} n}}}\implies a^{{\color{red} n}} \)

Answer 4

hmm?

Answer 5

notice, same base, different exponent
keep the base, sum the exponents

Answer 6

14

Answer 7

@jdoe0001

Answer 8

yeap \(\bf \cfrac{7^{-3}\cdot 7^9}{7^{-8}}\implies \cfrac{7^{-3}\cdot 7^9}{1}\cdot \cfrac{1}{7^{-8}}\implies 7^{-3}\cdot 7^9\cdot 7^{\color{brown}{ +8}}
\\ \quad \\
7^{-3+9+8}\implies 7^{14}\)