Which of the following is developed to be equivalent to 1/8^5?

Question

8^-5
8 1/5
5^-8
8^5

Answer 1

To find an expression equivalent to \( \frac{1}{8^5} \), we can rewrite it using the properties of exponents.

The expression \( \frac{1}{8^5} \) can be rewritten as:

\[ 8^{-5} \]

Now let's look at the options you provided:

1. \( 8^{-5} \)
2. \( 8^{1/5} \)
3. \( 5^{-8} \)
4. \( 8^5 \)

The first option, \( 8^{-5} \), is indeed equivalent to \( \frac{1}{8^5} \).

Therefore, the correct answer is:

8^-5

Answer 2

Which of the following is equivalent to 6^-2?
1/2^6
1/6^-2
1/36
36

Answer 3

To find an expression equivalent to \( 6^{-2} \), we can start by rewriting it using the properties of exponents.

The expression \( 6^{-2} \) can be rewritten as:

\[ 6^{-2} = \frac{1}{6^2} \]

Now, \( 6^2 = 36 \), so we have:

\[ 6^{-2} = \frac{1}{36} \]

Now let's evaluate the options you provided:

1. \( \frac{1}{2^6} \)
2. \( \frac{1}{6^{-2}} \) (which is equal to \( 6^2 = 36 \))
3. \( \frac{1}{36} \)
4. \( 36 \)

The third option, \( \frac{1}{36} \), is equivalent to \( 6^{-2} \).

Therefore, the correct answer is:

1/36

Answer 4

Which of the following is an equivalent expression to 13^-5 times 13^-11 with only positive exponents, generated by applying the properties of exponents?
1/26^6
1/26^16
1/13^6
1/13^16

Answer 5

To simplify the expression \( 13^{-5} \times 13^{-11} \) and express it using only positive exponents, we can apply the properties of exponents. Specifically, we use the rule that states:

\[ a^m \times a^n = a^{m+n} \]

Applying this to our expression:

\[ 13^{-5} \times 13^{-11} = 13^{-5 + (-11)} = 13^{-16} \]

Now, to express \( 13^{-16} \) with only positive exponents, we can use the property:

\[ a^{-n} = \frac{1}{a^n} \]

Thus, we have:

\[ 13^{-16} = \frac{1}{13^{16}} \]

Now, let's analyze the options provided:

1. \( \frac{1}{26^6} \)
2. \( \frac{1}{26^{16}} \)
3. \( \frac{1}{13^{6}} \)
4. \( \frac{1}{13^{16}} \)

The option that correctly represents our result is:

1/13^16