Question

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

3 over 2
3 to the power of 2 over 2 to the power of 2
3 to the power of 2 over 2
2 to the power of 4 over 3

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}}354−24−33442 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}}354−24−33442=3543423442

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}}3543423442=354342+234=35434434

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}35434434=44−334−5=4∗3−1=34

Answer 2

Given:

3 to the power of negative 4 multiplied by 2 to the power of 3 multiplied by 3 to the power of 2 whole over 2 to the power of 4 multiplied by 3 to the power of negative 3.

To find:

Simplified expression.

Solution:

3 to the power of negative 4 = 3⁻⁴

2 to the power of 3 = 2³

3 to the power of 2 = 3²

2 to the power of 4 = 2⁴

3 to the power of negative 3 = 3⁻³

According to the question,

3⁻⁴ multiplied by 2³ = 3⁻⁴ × 2³

2³ multiplied by 3² = 2³ × 3²

This can be written as,  3⁻⁴ × 2³ × 3²

3⁻⁴ × 2³ × 3² whole over 2⁴ multiplied by 3⁻³ = $\frac{3^{-4}*2^{3}*3^{2} }{2^{4} *3^{-3} }$

2³ and 2⁴ will be cancelled leaving with 2 in denominator.

3⁻³, 3² and 3⁻⁴ will be cancelled leaving with 3 in the numerator which gives $\frac{3^{-4}*2^{3}*3^{2} }{2^{4} *3^{-3} }=\frac{3}{2}$ i.e., 3 over 2.

3 over 2 is the simplified expression obtained. Hence, first option is the correct answer.