Question

What is the value of the expression shown below when a = 3 and b = 4 ?

(a^2b^-3)(a^-3b^4)

Select one:
A. 4/3
B. 1
C. 3
D. 4

Answer 1

\(\bf (a^2b^{-3})(a^{-3}b^4)\qquad a={\color{red}{ 3}}\qquad b={\color{blue}{ 4}}\implies ({\color{red}{ 3}}^2{\color{blue}{ 4}}^{-3})({\color{red}{ 3}}^{-3}{\color{blue}{ 4}}^4)
\\ \quad \\
\textit{keep in mind that } x^{-{\color{red} n}} = \cfrac{1}{x^{\color{red} n}}\)

Answer 2

so a?

Answer 3

hmm dunno... what did you get?

Answer 4

i got 242.25 and i know that isnt the answer

Answer 5

\(\bf (a^2b^{-3})(a^{-3}b^4)\qquad a={\color{red}{ 3}}\qquad b={\color{blue}{ 4}}\implies ({\color{red}{ 3}}^2{\color{blue}{ 4}}^{-3})({\color{red}{ 3}}^{-3}{\color{blue}{ 4}}^4)
\\ \quad \\
\textit{keep in mind that } a^{-{\color{red} n}} = \cfrac{1}{a^{\color{red} n}}\qquad thus
\\ \quad \\
({\color{red}{ 3}}^2{\color{blue}{ 4}}^{-3})({\color{red}{ 3}}^{-3}{\color{blue}{ 4}}^4)\implies \Large \left({\color{red}{ 3}}^2\cdot \frac{1}{{\color{blue}{ 4}}^3}\right)\left(\frac{1}{{\color{red}{ 3}}^3}\cdot {\color{blue}{ 4}}^4\right)\)

Answer 6

so (6 x 1/64)(1/27 x 256)?

Answer 7

yeap

Answer 8

i got 4.5

Answer 9

@jdoe0001

Answer 10

hmm well

Answer 11

https://www.google.com/search?client=opera&rls=en&q=3%5E2*(1/4%5E3)*(1/3%5E3)*4%5E4&sourceid=opera&ie=utf-8&oe=utf-8&channel=suggest

Answer 12

so its A?

Answer 13

yeap

Answer 14

have you covered the exponent rules yet?

Answer 15

a little

Answer 16

ok... notice using the exponent rules

\(\bf ({\color{red}{ 3}}^2{\color{blue}{ 4}}^{-3})({\color{red}{ 3}}^{-3}{\color{blue}{ 4}}^4)\implies 3^2\cdot 3^{-3}\cdot 4^{-3}\cdot 4^4\implies 3^{2-3}\cdot 4^{-3+4}
\\ \quad \\
3^{-1}\cdot 4^1\implies \cfrac{1}{3^1}\cdot 4\implies \cfrac{4}{3}\)

Answer 17

oh ok