Asked by JL

solve and leave in exponential form: 3^7 * 3^ -9 =

3^2
3^3
3^-7
3^-2
Answered by JL
What is this the solution as a whole number: 2^2 / 2^-4

-64
-46
64
46
Answered by JL
Apply the properties of Integer Exponents and find the simplified answer.

4^0 * 5^-2 / (-2)^-3

5/25
-8/25
-25/5
8/25
Answered by JL
Use the Properties of Integer Exponents to generate equivalent expressions with only positive exponents. Your answer will be a simplified fraction.

(14^3 * 27^-7)^0 / 3^4

-1/12
-81
1/81
12
Answered by JL
Pick one of the correct answers.
Answered by JL
Apply the Properties of Integer Exponents to generate equivalent expressions with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.

(4^3 * 7^-2)^-5 / 7^9 * 4^-13

7/16
21/28
-7/16
16
Answered by GPT 3.5
To solve the expression 3^7 * 3^(-9) and leave in exponential form, we can use the rule of exponents that states:

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

Applying this rule to the given expression, we get:

3^7 * 3^(-9) = 3^(7 + (-9))

Simplifying:

3^(-2)

Therefore, the expression 3^7 * 3^(-9) can be written in exponential form as 3^(-2).
Answered by GPT 3.5
To solve the expression 2^2 / 2^(-4) and find the solution as a whole number, we can use the rule of exponents that states:

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

Thus, using this rule in the given expression, we have:

2^2 / 2^(-4) = 2^(2 - (-4)) = 2^(2 + 4)

Simplifying:

2^6 = 64

Therefore, the solution to the expression 2^2 / 2^(-4) as a whole number is 64.
Answered by GPT 3.5
To simplify the expression 4^0 * 5^-2 / (-2)^-3, we can apply the properties of integer exponents.

First, let's evaluate each term separately:
4^0 = 1 (Any number raised to the power of 0 equals 1)
5^-2 = 1/5^2 = 1/25 (Negative exponent indicates reciprocal)
(-2)^-3 = 1/(-2)^3 = 1/(-8) = -1/8 (Negative exponent indicates reciprocal)

Now we substitute these values back into the original expression:
1 * (1/25) / (-1/8)

To divide fractions, we multiply by the reciprocal of the denominator:
1 * (1/25) * (-8/-1) = 8/25

Therefore, the simplified answer to the expression 4^0 * 5^-2 / (-2)^-3 is 8/25.
Answered by GPT 3.5
To generate equivalent expressions with only positive exponents, we can apply the properties of integer exponents:

First, we can simplify the expression within the parentheses:
14^3 / 27^7 becomes (14^3 / (3^3)^7)

Using the property of exponents (a^m)^n = a^(m*n), we can simplify further:
14^3 / (3^3 * 7)

Next, we can simplify the expression outside of the parentheses:
(14^3 * 27^-7)^0 can be simplified to 1 because any number raised to the power of 0 equals 1.

Now, we can substitute the simplified expressions back into the original expression:
1 / (14^3 / (3^3 * 7) ) * 3^4

To divide by a fraction, we multiply by the reciprocal:
1 * (3^3 * 7) / (14^3) * 3^4

Using the rule of exponents (a^m * a^n = a^(m + n)), we can simplify further:
(3^3 * 7 * 3^4) / (14^3)

Simplifying the numerator:
(27 * 7 * 81) / (14^3) = 15309 / (14^3)

Therefore, the simplified fraction equivalent to the original expression is 15309 / (14^3).
Answered by GPT 3.5
I apologize for the confusion. The simplified fraction equivalent to the original expression is 1/81.
Answered by GPT 3.5
To generate equivalent expressions with only positive exponents, we can apply the properties of integer exponents:

First, let's simplify the expression within the parentheses:
(4^3 * 7^-2)^-5 becomes (4^3 / 7^2)^-5

Using the property of exponents (a^m)^n = a^(m*n), we can simplify further:
(4^3 / 7^2)^-5 = (4^(3*-5) / 7^(2*-5))

Simplifying further:
4^-15 / 7^-10 = 1 / (4^15 * 7^10)

Now let's simplify the expression outside of the parentheses:
7^9 * 4^-13 becomes (7^9 / 4^13)

Substituting the simplified expressions back into the original expression:
(1 / (4^15 * 7^10)) * (7^9 / 4^13)

To multiply fractions, we multiply the numerators and the denominators separately:
(7^9 * 1) / (4^13 * 4^15 * 7^10)

Simplifying further:
7^9 / (4^13 * 4^15 * 7^10)

Using the property of exponents (a^m * a^n = a^(m + n)), we can simplify further:
7^9 / (4^(13 + 15) * 7^10)

Simplifying the exponent:
7^9 / (4^28 * 7^10)

Now, let's simplify the expression with the same base (7) using the property a^m / a^n = a^(m - n):
7^(9 - 10) / 4^28

Simplifying the exponents:
7^-1 / 4^28

Since 7^-1 is equal to 1/7, the expression becomes:
(1/7) / 4^28

To divide by a fraction, we multiply by the reciprocal:
1 / (7 * 4^28)

Simplifying the denominator:
1 / (7 * (2^2)^28) = 1 / (7 * 2^56)

Finally, we have the simplified fraction:
1 / (7 * 2^56) which cannot be simplified further.

Therefore, the answer is 1 / (7 * 2^56).