3 to the power of negative 4 as a fraction

Asked by admin @ 02/08/2021 in Math viewed by 284 People

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

Answered by admin @ 02/08/2021

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

3 to the power of negative 4 as a fraction

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