To solve 6^-4 using the properties of integer exponents, we can apply the property that states that a negative exponent can be written as the reciprocal of the positive exponent. Therefore:
6^-4 = 1/6^4
Now, we simplify 6^4:
6^4 = 6 * 6 * 6 * 6 = 1296
Now, substituting this result back into the equation:
1/6^4 = 1/1296
So, the answer is A. 1/1296.
Apply the Properties of Integer Exponents to solve 6^-4. The answer should not contain any exponent expression of decimals.
A. 1/1296
B. 2
C. 6/4
D. 1/216
7 answers
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 2^-13/5^-12 with positive exponents only.
A. 5^12/2^1
B. 2^13/5^12
C. 5^12/2^13
D. 3^-1
A. 5^12/2^1
B. 2^13/5^12
C. 5^12/2^13
D. 3^-1
To generate an expression equivalent to 2^-13/5^-12 with positive exponents only, we can apply the property of negative integer exponents.
The property states that for any nonzero number a, a^(-b) = 1/a^b.
Using this property, we can rewrite the expression:
2^-13/5^-12 = (1/2^13)/(1/5^12)
= 5^12/2^13
Therefore, the equivalent expression with positive exponents only is option C. 5^12/2^13.
The property states that for any nonzero number a, a^(-b) = 1/a^b.
Using this property, we can rewrite the expression:
2^-13/5^-12 = (1/2^13)/(1/5^12)
= 5^12/2^13
Therefore, the equivalent expression with positive exponents only is option C. 5^12/2^13.
Apply the product rule of integer exponents to find the numerical equivalent of 7^-11 × 7^13. Show your work and explain how you used the product rule of integer exponents.
The product rule of integer exponents states that when multiplying two exponential expressions with the same base, you can add their exponents together.
To find the numerical equivalent of 7^-11 × 7^13, we can use the product rule.
First, let's write out the expression using the product rule:
7^-11 × 7^13 = 7^(-11 + 13)
Now, let's simplify the exponent:
-11 + 13 = 2
Therefore, the expression simplifies to:
7^2
Calculating 7^2:
7^2 = 7 × 7 = 49
So, the numerical equivalent of 7^-11 × 7^13 is 49.
To find the numerical equivalent of 7^-11 × 7^13, we can use the product rule.
First, let's write out the expression using the product rule:
7^-11 × 7^13 = 7^(-11 + 13)
Now, let's simplify the exponent:
-11 + 13 = 2
Therefore, the expression simplifies to:
7^2
Calculating 7^2:
7^2 = 7 × 7 = 49
So, the numerical equivalent of 7^-11 × 7^13 is 49.
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