Question

Which of the following is equivalent to 3^−4

Answer 1

Please show work
Which of the following is equivalent to 3^−4

Answer 2

Apply the Zero Power Rule to create an equivalent expression to

(−40)^0 + 1/2 (11−32^0)

(2 points)
(−40)^0 + 1/2(11−32^0) = ? + 1/2 (? - ?)

Answer 3

Use the Product Rule of Exponents to simplify 3^5⋅3^7
Show steps

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Answer 4

can you show the adding

Answer 5

1/3^4 or 1/81

Answer 6

To simplify this expression, remember that a negative exponent can be rewritten as the reciprocal of the positive exponent.
So, 3^(-4) = 1/(3^4)

Now, let's evaluate 3^4:
3^4 = 3 * 3 * 3 * 3 = 81

Therefore, 3^(-4) = 1/81.

Answer 7

According to the Zero Power Rule, any non-zero number raised to the power of zero equals 1. Therefore, we have:

(-40)^0 = 1

Now let's simplify the second part of the expression:

32^0 = 1 (since any number raised to the power of 0 equals 1)

Now we can substitute these values back into the original expression:

(-40)^0 + 1/2(11-32^0) = 1 + 1/2(11-1)

Simplifying further:

(-40)^0 + 1/2(11-32^0) = 1 + 1/2(10)

Multiplying 1/2 by 10:

(-40)^0 + 1/2(11-32^0) = 1 + 5

Therefore, the simplified expression is:

(-40)^0 + 1/2(11-32^0) = 6

Answer 8

The Product Rule of Exponents states that when multiplying two powers with the same base, we can add their exponents.

To simplify 3^5 * 3^7, we can add the exponents:

3^5 * 3^7 = 3^(5+7)

Now, we can add the exponents:

3^(5+7) = 3^12

Therefore, 3^5 * 3^7 is equivalent to 3^12.

Answer 9

Certainly! To show the adding of exponents step-by-step, we have:

3^5 * 3^7

We want to simplify this expression by adding the exponents of 3.

First, let's write out the expanded form:

3^5 = 3 * 3 * 3 * 3 * 3
3^7 = 3 * 3 * 3 * 3 * 3 * 3 * 3

Now, let's combine the terms:

3^5 * 3^7 = (3 * 3 * 3 * 3 * 3) * (3 * 3 * 3 * 3 * 3 * 3 * 3)

By multiplying, we can see that we have a total of 12 3's:

(3 * 3 * 3 * 3 * 3) * (3 * 3 * 3 * 3 * 3 * 3 * 3) = 3^12

Therefore, 3^5 * 3^7 is equivalent to 3^12.