Apply the property of negative integer exponents to solve 7-3 . Your answer should be in fraction form and you will need to solve the exponent.(1 poi
To solve the expression 7^-3, we can use the property of negative exponents, which states that a negative exponent can be rewritten as the reciprocal of the corresponding positive exponent.
So, 7^-3 can be rewritten as 1/(7^3).
Calculating 7^3, we get 7 x 7 x 7 = 343.
Therefore, 7^-3 is equal to 1/343.
So, the solution to 7^-3 is 1/343.
ply the Property of Negative Integer Exponents to generate an expression equivalent to with positive exponents only.(1 point)
To generate an expression equivalent to 7^-3 with positive exponents only, we can apply the property of negative exponents, which states that a negative exponent can be rewritten as the reciprocal of the corresponding positive exponent.
So, 7^-3 can be rewritten as 1/(7^3).
However, this expression still contains a negative exponent. To convert it to positive exponents only, we can apply the property of reciprocals, which states that the reciprocal of a fraction is found by flipping the numerator and the denominator.
So, 1/(7^3) can be rewritten as (7^3)^-1.
By applying the property of raising a power to a power, we can simplify (7^3)^-1:
(7^3)^-1 = 7^(3*-1) = 7^-3.
Therefore, the expression equivalent to 7^-3 with positive exponents only is (7^3)^-1.
Apply the Properties of Integer Exponents to generate an equivalent expression for the following expression using only positive exponents, then solve the expression. Your answer should be an improper fraction. Hint: You will need to use the Power Rule, the Product Rule, and the Negative Exponent Rule. (1 point)
The given expression is 3^-2 * 2^-4 / 6^3.
To generate an equivalent expression with only positive exponents, we can apply the rules of integer exponents:
1) Power Rule: (a^m)^n = a^(m*n)
2) Product Rule: a^m * a^n = a^(m+n)
3) Negative Exponent Rule: a^-n = 1/a^n
So let's simplify the expression step by step:
3^-2 * 2^-4 / 6^3
Using the negative exponent rule, we can rewrite 3^-2 as 1/3^2, and 2^-4 as 1/2^4:
(1/3^2) * (1/2^4) / 6^3
Now applying the power rule, we can solve the expressions in the numerator and denominator for 3^2 and 2^4 respectively:
(1/9) * (1/16) / 6^3
Simplifying further, we have:
(1/9) * (1/16) / (6 * 6 * 6)
Multiplying the numerators and the denominator:
1/144 / (216)
Now, dividing the numerator by the denominator:
1/144 / 216 = 1/144 * 1/216 = 1/(144 * 216) = 1/31104
So the solution to the expression 3^-2 * 2^-4 / 6^3 with only positive exponents is 1/31104, which is an improper fraction.
Apply the product rule of integers exponents to find the numerical value of 12-5 * 127.(1 point)
To apply the product rule of integer exponents to find the numerical value of 12^-5 * 127, we need to evaluate each term separately and then multiply them together.
12^-5 = 1/(12^5) = 1/248,832
Now we can multiply this value by 127:
(1/248,832) * 127 = 127/248,832
So the numerical value of 12^-5 * 127 is 127/248,832.