solve 7^-3 using the property of negative integer exponents. don't include any exponent expression or decimals
To solve 7^-3 using the property of negative integer exponents, we can rewrite it as the reciprocal of 7^3:
7^-3 = 1/7^3
Now, let's evaluate 7^3:
7^3 = 7 * 7 * 7 = 343
Therefore,
7^-3 = 1/7^3 = 1/343
So, 7^-3 is equal to 1/343.
make an expression equivalent to 3^-17/8^-14 using the property of negative integer exponents. use positive exponents only
To simplify the expression 3^-17/8^-14 using the property of negative integer exponents and positive exponents only, we can apply the rule that states a^(-b) is equal to 1/a^b:
3^-17/8^-14 = (1/3^17)/(1/8^14)
Now, let's simplify the expression further:
(1/3^17)/(1/8^14) = (8^14)/(3^17)
This expression is equivalent to 8^14/3^17 using positive exponents only.
make an expression equivalent to 3^-17/8^-14 using the property of negative integer exponents. include only positive exponents in your answer.
To simplify the expression 3^-17/8^-14 using the property of negative integer exponents and including only positive exponents, we can apply the rule that states a^(-b) is equal to 1/a^b:
3^-17/8^-14 = (1/3^17)/(1/8^14)
Now, let's simplify the expression further:
(1/3^17)/(1/8^14) = (8^14)/(3^17)
To convert this expression to positive exponents, we can rewrite it as:
(8^14)/(3^17) = 8^14 * (1/3^17)
So, the expression equivalent to 3^-17/8^-14 using only positive exponents is 8^14 * (1/3^17).
make an expression equivalent to (7^-3)^7 multiplied by 7^20/6^-2 using the properties of integer exponents, then solve the expression. provide your answer as an improper fraction.
To solve the expression (7^-3)^7 multiplied by 7^20/6^-2 using the properties of integer exponents, we can apply the rules of multiplication and division with exponents.
First, let's simplify (7^-3)^7:
(7^-3)^7 = 7^((-3) * 7) = 7^-21
Next, let's simplify 7^20/6^-2:
7^20/6^-2 = 7^20 * (1/6^-2) = 7^20 * 6^2
Now, let's multiply these two expressions:
7^-21 * 7^20 * 6^2
Using the rule of addition with exponents, we can combine the exponents of 7:
7^(-21 + 20) * 6^2 = 7^-1 * 6^2
Now, let's simplify further:
7^-1 * 6^2 = 1/7 * 6^2 = 1/7 * 36 = 36/7
Therefore, the expression (7^-3)^7 multiplied by 7^20/6^-2 simplifies to the improper fraction 36/7.
Apply the product rule of integer exponents to find the numerical equivalent of 12^−5⋅12^7 . Show your work and explain how you used the product rule of integer exponents.(2 points)
The product rule of integer exponents states that when multiplying two powers with the same base, you can add their exponents.
In the expression 12^(-5) * 12^7, we have the same base, which is 12. Therefore, we can apply the product rule and add the exponents:
12^(-5) * 12^7 = 12^(-5 + 7)
Simplifying the exponent:
12^(-5 + 7) = 12^2
Now, we can evaluate 12^2:
12^2 = 12 * 12 = 144
So, the numerical equivalent of 12^(-5) * 12^7 is 144.
To solve 7^-3 using the property of negative exponents, we can apply the following rule:
A negative exponent on a non-zero base is equivalent to the reciprocal of the base raised to the positive exponent.
So, in this case, we have 7^-3.
Step 1: Take the reciprocal of 7, which is 1/7.
Step 2: Raise the reciprocal to the positive exponent, which is 3.
Step 3: Simplify the expression.
Therefore, 7^-3 can be written as 1/(7^3) or 1/343.
So, the answer is 1/343 without using any exponent expression or decimals.