Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7−3⋅7−5 with positive exponents only.
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 5−9/4−12 with positive exponents only
The Property of Negative Integer Exponents states that a negative exponent can be rewritten as the reciprocal of the corresponding positive exponent.
Applying this property to the expression 7^-3 ⋅ 7^-5, we get:
7^-3 ⋅ 7^-5 = 1/7^3 ⋅ 1/7^5
To simplify further, we can combine the fractions:
1/7^3 ⋅ 1/7^5 = 1/(7^3 ⋅ 7^5)
Using the property of multiplying exponents with the same base, we can add the exponents:
7^3 ⋅ 7^5 = 7^(3+5) = 7^8
Therefore, the expression equivalent to 7^-3 ⋅ 7^-5 with positive exponents only is 1/7^8.
To apply the Property of Negative Integer Exponents, we need to rewrite the negative exponents as the reciprocal of the corresponding positive exponents.
Using this property, let's rewrite the given expression:
5^(-9/4) ⋅ 4^(-12)
Since the exponent is -9/4, we can rewrite it as the reciprocal of the positive exponent:
1/5^(9/4) ⋅ 1/4^12
To simplify the expression further, we can take the fourth root of both the numerator and denominator to get rid of the fractional exponent:
1/∛(5^9) ⋅ 1/4^12
Finally, we can rewrite the cube root of 5^9 as (5^9)^(1/3), which is equal to 5^(9/3) = 5^3:
1/5^3 ⋅ 1/4^12
The expression equivalent to 5^(-9/4) ⋅ 4^(-12) with positive exponents only is therefore 1/5^3 ⋅ 1/4^12.
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 5−9/4−12 with positive exponents only
5−9/4−12=
To apply the Property of Negative Integer Exponents, we need to rewrite the negative exponents as the reciprocal of the corresponding positive exponents.
Using this property, let's rewrite the given expression:
5^(-9/4) ⋅ 4^(-12)
Since the exponent is -9/4, we can rewrite it as the reciprocal of the positive exponent:
1/5^(9/4) ⋅ 1/4^12
Now, let's simplify the expression further. Taking the fourth root of both the numerator and denominator allows us to get rid of the fractional exponent:
1/∜(5^9) ⋅ 1/4^12
Finally, we can rewrite the fourth root of 5^9 as (5^9)^(1/4), which is equal to 5^(9/4):
1/5^(9/4) ⋅ 1/4^12
The expression equivalent to 5^(-9/4) ⋅ 4^(-12) with positive exponents only is therefore 1/5^(9/4) ⋅ 1/4^12.
Which of the following is developed to be equivalent to 1/8 5?(1 point)
5− 8
8 5
8 1/5
8− 5
The expression developed to be equivalent to 1/8 * 5 is:
8^-5
Which of the following is equivalent to 6−2?
1/2 6
1/36
36
1/6 −2
The expression equivalent to 6^-2 is 1/36.
To generate an expression equivalent to 7^(-3) * 7^(-5) with positive exponents only, we can apply the property of negative integer exponents, which states that a^(-n) is equal to 1/a^n.
Let's use this property:
7^(-3) * 7^(-5) = (1/7^3) * (1/7^5)
Now, to simplify, we can combine the fractions by multiplying the numerators and denominators:
(1/7^3) * (1/7^5) = 1/((7^3) * (7^5))
Next, we can use the property of exponents to simplify the expression further. When multiplying two exponents with the same base, you can add their exponents:
1/((7^3) * (7^5)) = 1/(7^(3+5))
Simplifying the exponent:
1/(7^8)
Thus, the expression equivalent to 7^(-3) * 7^(-5) with positive exponents only is 1/(7^8).