Answer:
4/3
Step-by-step explanation:
You can simplify the exponent expression using exponent rules. The rules are:
- A positive exponent is the number of times the base multiplies by itself.
- A negative exponent is the number of times the base divides itself.
- Multiplying same bases with exponents is simplified by adding the exponents.
- Dividing same bases with exponents is simplified by subtracting the exponents.
- A zero exponent always evaluates as 1.
The expression [tex]\frac{4^{-3}3^44^2}{3^54^{-2}}[/tex] can be simplified first using the negative exponent rule to move base with negative exponent to the other part of the fraction.
[tex]\frac{4^{-3}3^44^2}{3^54^{-2}} = \frac{4^{2}3^44^2}{3^54^{3}}[/tex]
Now use the multiplication rule to simplify numerator and denominator.
[tex]\frac{4^{2}3^44^2}{3^54^{3}} = \frac{4^{2+2}3^4}{3^54^{3}} = \frac{4^{4}3^4}{3^54^{3}}[/tex]
Finally, use the division rule to reduce the fraction.
[tex]\frac{4^{4}3^4}{3^54^{3}}= 4^{4-3} 3^{4-5} = 4*3^{-1} = \frac{4}{3}[/tex]
