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.
3^7 . 3^-9 = ___
To apply the properties of integer exponents and generate equivalent expressions with only positive exponents, we can use the rule that states ``a^m . a^n = a^(m + n)".
Using this rule, we can rewrite the expression as:
3^7 . 3^-9 = 3^(7 + (-9))
Simplifying the exponent, we get:
3^(7 + (-9)) = 3^-2
Now, we know that a negative exponent indicates the reciprocal of the positive exponent. Therefore, 3^-2 is equal to 1 / 3^2.
Simplifying further, we have:
3^-2 = 1 / 3^2 = 1 / 9
So, 3^7 . 3^-9 is equivalent to 1 / 9.
apply the Properties of Integer Exponents to generate equivalent expressions to 2^2/2^-4 with only positive exponents, then solve the expression. provide the solution as a whole number.
2^2/2^-4 = ___
To apply the properties of integer exponents and generate equivalent expressions with only positive exponents, we can use the rule that states ``a^m / a^n = a^(m - n)".
Using this rule, we can rewrite the expression as:
2^2 / 2^-4 = 2^(2 - (-4))
Simplifying the exponent, we get:
2^(2 - (-4)) = 2^6
So, 2^2 / 2^-4 is equivalent to 2^6.
To solve this expression and provide the answer as a whole number, we can simplify the exponent:
2^6 = 2 * 2 * 2 * 2 * 2 * 2 = 64
Therefore, 2^2 / 2^-4 equals 64.
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 simplified fraction with no remaining exponents.
4^0 . 5^-2/(-2)^-3 = ____
To apply the properties of integer exponents and generate equivalent expressions with only positive exponents, we can use the following rules:
1. Any number raised to the power of 0 is equal to 1: a^0 = 1.
2. To convert a negative exponent to a positive exponent, we can take the reciprocal of the base with the positive exponent: a^-n = 1/a^n.
Now, let's simplify each term one by one:
1. 4^0: Using rule 1, 4^0 = 1.
2. 5^-2: Using rule 2, 5^-2 = 1/5^2 = 1/25.
3. (-2)^-3: Using rule 2, (-2)^-3 = 1/(-2)^3 = 1/(-8) = -1/8.
Putting all the simplified terms together, we have:
4^0 . 5^-2/(-2)^-3 = 1 * (1/25) / (-1/8) = (1/25) / (-1/8) = (1/25) * (-8/1) = -8/25.
Therefore, the simplified fraction for 4^0 . 5^-2/(-2)^-3 is -8/25.
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 simplified fraction with no remaining exponents.
(14^3 . 27^-7)^0/3^4 = _____
To apply the properties of integer exponents and generate equivalent expressions with only positive exponents, we can use the following rules:
1. Any number raised to the power of 0 is equal to 1: a^0 = 1.
2. To convert a negative exponent to a positive exponent, we can take the reciprocal of the base with the positive exponent: a^-n = 1/a^n.
3. When raising a power to another power, we multiply the exponents: (a^m)^n = a^(m * n).
Now, let's simplify each term one by one:
1. (14^3 . 27^-7)^0: According to rule 1, any expression raised to the power of 0 is equal to 1.
2. 3^4: No further simplification is needed for 3^4, as it is already in positive exponent form.
Combining the simplified terms, we have:
(14^3 . 27^-7)^0 / 3^4 = 1 / 3^4 = 1 / (3^2 * 3^2) = 1 / (9 * 9) = 1 / 81.
Therefore, the simplified fraction for (14^3 . 27^-7)^0 / 3^4 is 1/81.