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.