What makes the statement true? 8-^2=?

64****
16
-1/26
1/64

Evaluate the expression 4-^2x2^0
8
16***
1/16
-64

Write 5^2•5-^1•5^3 as a single exponent
5^4
5-^6****
5^5
5^2

8^-2 = 1/8^2 = 1/64

4^-2 * 2^0 = 1/16 * 1 = 1/16
5^(2-1+3) = 5^4

Your typos make things hard to read

To find the answer to the first question, "What makes the statement true? 8-^2=?", we need to understand the rules of exponentiation.

In mathematics, an exponent, represented by the "^" symbol, indicates how many times a number is multiplied by itself. For example, 2^2 means 2 multiplied by itself twice, which is equal to 4.

Now, let's look at the options given:

- 64: This is not the correct answer because 8^2 is equal to 64, not 8-^2.
- 16: This is not the correct answer because 8^2 is equal to 64, not 8-^2.
- -1/26: This is not the correct answer because it is unrelated to the expression 8-^2.
- 1/64: This is the correct answer because 8-^2 is equal to 1/64. By applying the rules of exponentiation, we find that 8-^2 is the same as 8^(-2), which means 8 divided by itself twice. When we divide 8 by itself twice, we get 1/64.

Moving on to the second question, "Evaluate the expression 4-^2x2^0":

To solve this expression, we follow the order of operations, which states that we should solve any exponentiation first, then perform multiplication and division from left to right, and finally perform addition and subtraction from left to right.

Let's break down the expression:

4-^2 can be rewritten as 4^(-2). In this case, raising a number to a negative exponent means taking the reciprocal of the number raised to the positive exponent. So, 4^(-2) is equal to 1/(4^2) or 1/16.

2^0 is equal to 1 because any number raised to the power of 0 is always 1.

Now, we can substitute the values back into the expression:

4^(-2) x 1/16 = 1/(4^2) x 1/16 = 1/16 x 1/16 = 1/256.

Therefore, the correct answer is 1/256.

Finally, for the third question, "Write 5^2•5-^1•5^3 as a single exponent":

To combine the exponents, we need to remember the rule that states when multiplying numbers with the same base, the exponents are added together.

Let's look at the options given:

- 5^4: This is not the correct answer because it does not simplify the expression 5^2•5-^1•5^3.
- 5-^6: This is the correct answer because 5^2•5-^1•5^3 simplifies to 5^(2+(-1)+3), which is equal to 5^4.
- 5^5: This is not the correct answer because it does not simplify the expression 5^2•5-^1•5^3.
- 5^2: This is not the correct answer because it does not simplify the expression 5^2•5-^1•5^3.

Therefore, the correct answer is 5-^6, which simplifies the given expression as a single exponent.