Apply the Property of Negative Integer Exponents to solve 3^−4
. The answer should not contain any exponent expression or decimals.
The property of negative integer exponents states that a non-zero number raised to a negative exponent is equal to the reciprocal of the same number raised to the positive exponent.
Applying this property to 3^−4, we get:
3^−4 = 1 / 3^4
Simplifying further,
1 / 3^4 = 1 / (3 * 3 * 3 * 3)
= 1 / 81
Therefore, 3^−4 = 1 / 81, and the answer does not contain any exponent expression or decimals.
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7−3⋅7−5
with positive exponents only.
The property of negative integer exponents states that a non-zero number raised to a negative exponent is equal to the reciprocal of the same number raised to the positive exponent.
Applying this property to 7^−3 and 7^−5, we get:
7^−3 = 1 / 7^3
7^−5 = 1 / 7^5
To generate an expression with positive exponents only, we can rewrite the given expression as:
7^−3 ⋅ 7^−5 = (1 / 7^3) ⋅ (1 / 7^5)
Using the properties of exponents, we can simplify this expression as follows:
(1 / 7^3) ⋅ (1 / 7^5) = 1 / (7^3 ⋅ 7^5) = 1 / 7^8
Therefore, an expression equivalent to 7−3⋅7−5 with positive exponents only is 1 / 7^8.
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 5−94−12
with positive exponents only.
To generate an expression equivalent to 5^-9 * 4^-12 with positive exponents only, we can apply the property of negative integer exponents which states that a non-zero number raised to a negative exponent is equal to the reciprocal of the same number raised to the positive exponent.
Using this property, we can rewrite 5^-9 as 1 / 5^9 and 4^-12 as 1 / 4^12.
Therefore, the expression 5^-9 * 4^-12 is equivalent to (1 / 5^9) * (1 / 4^12).
To simplify further, we can combine the fractions by multiplying the numerators and the denominators.
(1 / 5^9) * (1 / 4^12) = 1 / (5^9 * 4^12).
Therefore, an expression equivalent to 5^-9 * 4^-12 with positive exponents only is 1 / (5^9 * 4^12).
Which of the following is developed to be equivalent to 1/8^5?
To find an equivalent expression for 1/8^5, we can use the property of negative exponents which states that a non-zero number raised to a negative exponent is equal to the reciprocal of the same number raised to the positive exponent.
Applying this property to 1/8^5, we get:
1/8^5 = 8^-5
Therefore, an expression that is equivalent to 1/8^5 is 8^-5.
use a calculator
To find the value of 1/8^5 using a calculator:
1. Enter 1 ÷ 8^5 (or 1 / 8^5) into the calculator.
2. Press the "=" button to calculate the result.
The calculator should display the decimal equivalent of 1/8^5, which is approximately 1.2207e-06.
Which of the following is equivalent to 6^−2
To find an expression equivalent to 6^−2, we can use the property of negative exponents which states that a non-zero number raised to a negative exponent is equal to the reciprocal of the same number raised to the positive exponent.
Applying this property to 6^−2, we get:
6^−2 = 1/6^2
Therefore, an expression equivalent to 6^−2 is 1/6^2.
Which of the following is an equivalent expression to 13^−5 ⋅13^−11 with only positive exponents, generated by applying the properties of exponents?
To find an equivalent expression to 13^−5 ⋅ 13^−11 with only positive exponents, we can use the property of exponents that states that when multiplying two numbers with the same base, we can add their exponents together.
Using this property, we can rewrite the given expression as:
13^(-5 + -11)
Simplifying the exponents:
13^(-16)
Now, to rewrite the expression with positive exponents, we can use the property of negative exponents that states a non-zero number raised to a negative exponent is equal to the reciprocal of the same number raised to the positive exponent.
Therefore, an equivalent expression with positive exponents only to 13^−5 ⋅ 13^−11 is 1 / 13^16.
Which of the following is an equivalent expression to 14^−7/9^−13 with only positive exponents, generated by applying the Property of Negative Integer Exponents?
To find an equivalent expression to 14^−7/9^−13 with only positive exponents, we can apply the Property of Negative Integer Exponents, which states that a non-zero number raised to a negative exponent is equal to the reciprocal of the same number raised to the positive exponent.
Using this property, we can rewrite the given expression as follows:
14^−7/9^−13 = (1/14^7)/(1/9^13)
Next, we can use the property of division to simplify this expression:
(1/14^7)/(1/9^13) = (1/14^7) * (9^13/1)
Now, we only need to focus on the positive exponents in the expression. So, rewriting it as:
(9^13)/(14^7)
Therefore, an equivalent expression to 14^−7/9^−13 with only positive exponents, generated by applying the Property of Negative Integer Exponents, is 9^13/14^7.
Which of the following is an equivalent expression to 7^3/25^−4 with only positive exponents, generated by applying the Property of Negative Integer Exponents?
To find an equivalent expression to 7^3/25^−4 with only positive exponents, we can apply the Property of Negative Integer Exponents, which states that a non-zero number raised to a negative exponent is equal to the reciprocal of the same number raised to the positive exponent.
Using this property, we can rewrite the given expression as follows:
7^3/25^−4 = 7^3/(1/25^4)
Next, we can use the property of reciprocal to simplify this expression:
7^3/(1/25^4) = 7^3 * 25^4
Now, we have the expression with only positive exponents:
7^3 * 25^4
Therefore, an equivalent expression to 7^3/25^−4 with only positive exponents, generated by applying the Property of Negative Integer Exponents, is 7^3 * 25^4.