Question

Apply the Properties of Integer Exponents to solve 6^-4. The answer should not contain any exponent expression of decimals.
A. 1/1296
B. 2
C. 6/4
D. 1/216

Answer 1

Apply the Property of Negative Integer Exponents to generate an expression equivalent to 2^-13/5^-12 with positive exponents only.
A. 5^12/2^1
B. 2^13/5^12
C. 5^12/2^13
D. 3^-1

Answer 2

Apply the product rule of integer exponents to find the numerical equivalent of 7^-11 × 7^13. Show your work and explain how you used the product rule of integer exponents.

Answer 3

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Answer 4

To solve 6^-4 using the properties of integer exponents, we can apply the property that states that a negative exponent can be written as the reciprocal of the positive exponent. Therefore:

6^-4 = 1/6^4

Now, we simplify 6^4:

6^4 = 6 * 6 * 6 * 6 = 1296

Now, substituting this result back into the equation:

1/6^4 = 1/1296

So, the answer is A. 1/1296.

Answer 5

To generate an expression equivalent to 2^-13/5^-12 with positive exponents only, we can apply the property of negative integer exponents.

The property states that for any nonzero number a, a^(-b) = 1/a^b.

Using this property, we can rewrite the expression:

2^-13/5^-12 = (1/2^13)/(1/5^12)
= 5^12/2^13

Therefore, the equivalent expression with positive exponents only is option C. 5^12/2^13.

Answer 6

The product rule of integer exponents states that when multiplying two exponential expressions with the same base, you can add their exponents together.

To find the numerical equivalent of 7^-11 × 7^13, we can use the product rule.

First, let's write out the expression using the product rule:

7^-11 × 7^13 = 7^(-11 + 13)

Now, let's simplify the exponent:

-11 + 13 = 2

Therefore, the expression simplifies to:

7^2

Calculating 7^2:

7^2 = 7 × 7 = 49

So, the numerical equivalent of 7^-11 × 7^13 is 49.

Answer 7

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