Question

What is the simplified expression for 4 to the power of negative 3 multiplied by 3 to the power of 4 multiplied by 4 to the power of 2 whole over 3 to the power of 5 multiplied by 4 to the power of negative 2

Answer 1

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 $\frac{4^{-3}3^44^2}{3^54^{-2}}$ can be simplified first using the negative exponent rule to move base with negative exponent to the other part of the fraction.

$\frac{4^{-3}3^44^2}{3^54^{-2}} = \frac{4^{2}3^44^2}{3^54^{3}}$

Now use the multiplication rule to simplify numerator and denominator.

$\frac{4^{2}3^44^2}{3^54^{3}} = \frac{4^{2+2}3^4}{3^54^{3}} = \frac{4^{4}3^4}{3^54^{3}}$

Finally, use the division rule to reduce the fraction.

$\frac{4^{4}3^4}{3^54^{3}}= 4^{4-3} 3^{4-5} = 4*3^{-1} = \frac{4}{3}$

Answer 2

Answer:

4/3

Step-by-step explanation: