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).
solve and leave in exponential form: 3^7 * 3^ -9 =
3^2
3^3
3^-7
3^-2
11 answers
What is this the solution as a whole number: 2^2 / 2^-4
-64
-46
64
46
-64
-46
64
46
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.
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.
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
4^0 * 5^-2 / (-2)^-3
5/25
-8/25
-25/5
8/25
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.
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.
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
(14^3 * 27^-7)^0 / 3^4
-1/12
-81
1/81
12
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).
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).
Pick one of the correct answers.
I apologize for the confusion. The simplified fraction equivalent to the original expression is 1/81.
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
(4^3 * 7^-2)^-5 / 7^9 * 4^-13
7/16
21/28
-7/16
16
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).
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).
1 answer