Question
Apply the Properties of Integer Exponents to generate equivalent expressions to 3^7.3^-9 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.
Answers
Answer
Apply the Properties of Integer Exponents to generate equivalent expressions to (4 ^ 0 * 5 ^ - 2)/((- 2) ^ - 3) with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.
Answer
Apply the Properties of Integer Exponents to generate equivalent expressions to 4 ^ 0 * 5 ^ - 2/(- 2) ^ - 3 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.
Answer
Apply the Properties of Integer Exponents to generate equivalent expressions to (14^3*27^-7)^0/3^4 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.
Answered by
GPT 3.5
To generate equivalent expressions with only positive exponents, we can use the following properties:
1. Product of Powers Property: a^m * a^n = a^(m+n)
2. Quotient of Powers Property: a^m / a^n = a^(m-n)
3. Power of a Power Property: (a^m)^n = a^(m*n)
Using these properties, we can simplify the expression.
3^7.3^-9 = (3^7) * (3^-9) = (3^7) / (3^9)
Now, using the Quotient of Powers Property, we can rewrite the expression as:
(3^7) / (3^9) = 3^(7-9) = 3^-2
To get rid of the negative exponent, we can use the Power of a Power Property:
3^-2 = 1 / 3^2 = 1/9
Therefore, the simplified fraction equivalent to 3^7.3^-9 with only positive exponents is 1/9.
1. Product of Powers Property: a^m * a^n = a^(m+n)
2. Quotient of Powers Property: a^m / a^n = a^(m-n)
3. Power of a Power Property: (a^m)^n = a^(m*n)
Using these properties, we can simplify the expression.
3^7.3^-9 = (3^7) * (3^-9) = (3^7) / (3^9)
Now, using the Quotient of Powers Property, we can rewrite the expression as:
(3^7) / (3^9) = 3^(7-9) = 3^-2
To get rid of the negative exponent, we can use the Power of a Power Property:
3^-2 = 1 / 3^2 = 1/9
Therefore, the simplified fraction equivalent to 3^7.3^-9 with only positive exponents is 1/9.
Answered by
GPT 3.5
To generate equivalent expressions with only positive exponents, we can use the following properties:
1. Product of Powers Property: a^m * a^n = a^(m+n)
2. Quotient of Powers Property: a^m / a^n = a^(m-n)
3. Power of a Power Property: (a^m)^n = a^(m*n)
4. Negative Exponent Property: a^(-m) = 1/a^m
Let's simplify the expression step by step:
(4^0 * 5^-2) / ((-2)^-3)
Since any number raised to the power of 0 is equal to 1, we can simplify 4^0 as 1:
(1 * 5^-2) / ((-2)^-3)
Using the Negative Exponent Property, we can rewrite 5^-2 as 1/5^2:
(1 * 1/5^2) / ((-2)^-3)
So far, we have simplified the expression to:
1/5^2 / ((-2)^-3)
Using the Negative Exponent Property again, we can rewrite (-2)^-3 as 1/(-2)^3:
1/5^2 / 1/(-2)^3
Next, we can use the Quotient of Powers Property to divide 1/5^2 by 1/(-2)^3:
(1/5^2) * ((-2)^3/1)
Now, we can simplify the expression further:
(1/25) * (-8)
Multiplying the fractions, we get:
-8/25
Therefore, the simplified fraction equivalent to (4^0 * 5^-2)/((-2)^-3) with only positive exponents is -8/25.
1. Product of Powers Property: a^m * a^n = a^(m+n)
2. Quotient of Powers Property: a^m / a^n = a^(m-n)
3. Power of a Power Property: (a^m)^n = a^(m*n)
4. Negative Exponent Property: a^(-m) = 1/a^m
Let's simplify the expression step by step:
(4^0 * 5^-2) / ((-2)^-3)
Since any number raised to the power of 0 is equal to 1, we can simplify 4^0 as 1:
(1 * 5^-2) / ((-2)^-3)
Using the Negative Exponent Property, we can rewrite 5^-2 as 1/5^2:
(1 * 1/5^2) / ((-2)^-3)
So far, we have simplified the expression to:
1/5^2 / ((-2)^-3)
Using the Negative Exponent Property again, we can rewrite (-2)^-3 as 1/(-2)^3:
1/5^2 / 1/(-2)^3
Next, we can use the Quotient of Powers Property to divide 1/5^2 by 1/(-2)^3:
(1/5^2) * ((-2)^3/1)
Now, we can simplify the expression further:
(1/25) * (-8)
Multiplying the fractions, we get:
-8/25
Therefore, the simplified fraction equivalent to (4^0 * 5^-2)/((-2)^-3) with only positive exponents is -8/25.
Answered by
GPT 3.5
To generate equivalent expressions with only positive exponents, we can use the following properties:
1. Product of Powers Property: a^m * a^n = a^(m+n)
2. Quotient of Powers Property: a^m / a^n = a^(m-n)
3. Power of a Power Property: (a^m)^n = a^(m*n)
4. Negative Exponent Property: a^(-m) = 1/a^m
Let's simplify the expression step by step:
4^0 * 5^-2 / (-2)^-3
Since any number raised to the power of 0 is equal to 1, we can simplify 4^0 as 1:
1 * 5^-2 / (-2)^-3
Using the Negative Exponent Property, we can rewrite 5^-2 as 1/5^2:
1 * 1/5^2 / (-2)^-3
So far, we have simplified the expression to:
1/5^2 / (-2)^-3
Using the Negative Exponent Property again, we can rewrite (-2)^-3 as 1/(-2)^3:
1/5^2 / 1/(-2)^3
Next, we can rewrite the division as a multiplication by taking the reciprocal of the second fraction:
1/5^2 * (-2)^3/1
Now, we can simplify the expression further:
1/25 * (-8)
Multiplying the fractions, we get:
-8/25
Therefore, the simplified fraction equivalent to 4^0 * 5^-2 / (-2)^-3 with only positive exponents is -8/25.
1. Product of Powers Property: a^m * a^n = a^(m+n)
2. Quotient of Powers Property: a^m / a^n = a^(m-n)
3. Power of a Power Property: (a^m)^n = a^(m*n)
4. Negative Exponent Property: a^(-m) = 1/a^m
Let's simplify the expression step by step:
4^0 * 5^-2 / (-2)^-3
Since any number raised to the power of 0 is equal to 1, we can simplify 4^0 as 1:
1 * 5^-2 / (-2)^-3
Using the Negative Exponent Property, we can rewrite 5^-2 as 1/5^2:
1 * 1/5^2 / (-2)^-3
So far, we have simplified the expression to:
1/5^2 / (-2)^-3
Using the Negative Exponent Property again, we can rewrite (-2)^-3 as 1/(-2)^3:
1/5^2 / 1/(-2)^3
Next, we can rewrite the division as a multiplication by taking the reciprocal of the second fraction:
1/5^2 * (-2)^3/1
Now, we can simplify the expression further:
1/25 * (-8)
Multiplying the fractions, we get:
-8/25
Therefore, the simplified fraction equivalent to 4^0 * 5^-2 / (-2)^-3 with only positive exponents is -8/25.