Question

Apply the property of negative integer exponents to generate an expression equivalent to 7^-3•7^-5=? With positive exponents only.

Answer 1

Apply the property of negative integer exponents to generate an expression equivalent to 5^-9/4^-12 With positive exponents only.

Answer 2

What is equivalent to 1/8^5?

Answer 3

What is equivalent to 6^-2

Answer 4

13^-5•13^-11

Answer 5

What is equivalent to 14^-7/9^-13 with only positive exponents

Answer 6

What is equivalent to 7^3/25^-4 with only positive exponents

Answer 7

To apply the property of negative integer exponents and rewrite the expression with positive exponents only, we can use the rule that states:

a^(-m) = 1 / a^m

Let's apply this rule to the expression 7^(-3) * 7^(-5):

7^(-3) * 7^(-5) = (1 / 7^3) * (1 / 7^5)

Now, let's use the rule for multiplying fractions:

(1 / 7^3) * (1 / 7^5) = 1 / (7^3 * 7^5)

To simplify further, we can use the rule that states:

a^m * a^n = a^(m + n)

Using this rule, we can add the exponents:

7^3 * 7^5 = 7^(3 + 5) = 7^8

Therefore, 7^(-3) * 7^(-5) = 1 / 7^8

Answer 8

To rewrite the expression 5^-9/4^-12 with positive exponents only, we can use the property of negative integer exponents, which states:

a^-m = 1/a^m

Let's apply this property to the given expression:

5^-9 / 4^-12

Using the property, we can rewrite it as follows:

1/5^9 / 1/4^12

Now, let's simplify the expression using the rule of dividing fractions:

1/5^9 / 1/4^12 = 1/5^9 * 4^12/1

Next, let's use the property of negative integer exponents to transform 1/5^9 * 4^12 into positive exponents only:

1/5^9 * 4^12 = 4^12/5^9

Therefore, the expression 5^-9/4^-12 is equivalent to 4^12/5^9.

Answer 9

To find an expression equivalent to 1/8^5, we can use the property of negative exponents, which states:

a^-n = 1/a^n

Applying this property to the expression 1/8^5, we rewrite it as follows:

1/8^5 = 8^-5

Now, to transform 8^-5 into an expression with a positive exponent, we use the property of reciprocals:

a^-n = 1/a^n

Therefore, 8^-5 is equivalent to 1/8^5, and there is no expression with a positive exponent that is equivalent to 1/8^5.

Answer 10

To find an expression equivalent to 6^-2 with positive exponents only, we can use the property of negative exponents:

a^-n = 1/a^n

Applying this property to the expression 6^-2, we can rewrite it as:

1/6^2

Simplifying further, we have:

1/6^2 = 1/36

Therefore, 6^-2 is equivalent to 1/36.

Answer 11

To rewrite the expression 13^-5 • 13^-11 with positive exponents only, we can apply the property of negative exponents, which states:

a^-m = 1/a^m

Let's simplify the expression step by step:

13^-5 • 13^-11 = 1/13^5 • 1/13^11

Next, we can apply the rule for multiplying fractions:

1/13^5 • 1/13^11 = 1 / (13^5 • 13^11)

Using the rule for multiplying with the same base, we can add the exponents:

13^5 • 13^11 = 13^(5+11) = 13^16

Therefore, 13^-5 • 13^-11 is equivalent to 1/13^16.

Answer 12

To rewrite the expression 14^-7/9^-13 with positive exponents only, we can utilize the property of negative exponents:

a^-n = 1/a^n

Applying this property to the given expression, we have:

14^-7/9^-13 = (1/14^7)/(1/9^13)

To simplify further, we can multiply by the reciprocal of the denominator:

(1/14^7)/(1/9^13) = (1/14^7) * (9^13/1)

Now, using the rule of multiplying fractions:

(1/14^7) * (9^13/1) = 9^13/14^7

Therefore, the expression 14^-7/9^-13 is equivalent to 9^13/14^7.

Answer 13

To rewrite the expression 7^3/25^-4 with positive exponents only, we can utilize the property of negative exponents:

a^-n = 1/a^n

Applying this property to the given expression, we have:

7^3/25^-4 = 7^3/(1/25^4)

To simplify further, we can multiply by the reciprocal of the denominator:

7^3/(1/25^4) = 7^3 * (25^4/1)

Now, using the rule of multiplying fractions:

7^3 * (25^4/1) = 7^3 * 25^4

Therefore, the expression 7^3/25^-4 is equivalent to 7^3 * 25^4.