Apply the property of negative integer exponents to generate an expression equivalent to 7^-3•7^-5=? With positive exponents only.
To apply the property of negative integer exponents and rewrite the expression with positive exponents only, we can use the rule that states:
a^(-m) = 1 / a^m
Let's apply this rule to the expression 7^(-3) * 7^(-5):
7^(-3) * 7^(-5) = (1 / 7^3) * (1 / 7^5)
Now, let's use the rule for multiplying fractions:
(1 / 7^3) * (1 / 7^5) = 1 / (7^3 * 7^5)
To simplify further, we can use the rule that states:
a^m * a^n = a^(m + n)
Using this rule, we can add the exponents:
7^3 * 7^5 = 7^(3 + 5) = 7^8
Therefore, 7^(-3) * 7^(-5) = 1 / 7^8
Apply the property of negative integer exponents to generate an expression equivalent to 5^-9/4^-12 With positive exponents only.
To rewrite the expression 5^-9/4^-12 with positive exponents only, we can use the property of negative integer exponents, which states:
a^-m = 1/a^m
Let's apply this property to the given expression:
5^-9 / 4^-12
Using the property, we can rewrite it as follows:
1/5^9 / 1/4^12
Now, let's simplify the expression using the rule of dividing fractions:
1/5^9 / 1/4^12 = 1/5^9 * 4^12/1
Next, let's use the property of negative integer exponents to transform 1/5^9 * 4^12 into positive exponents only:
1/5^9 * 4^12 = 4^12/5^9
Therefore, the expression 5^-9/4^-12 is equivalent to 4^12/5^9.
What is equivalent to 1/8^5?
To find an expression equivalent to 1/8^5, we can use the property of negative exponents, which states:
a^-n = 1/a^n
Applying this property to the expression 1/8^5, we rewrite it as follows:
1/8^5 = 8^-5
Now, to transform 8^-5 into an expression with a positive exponent, we use the property of reciprocals:
a^-n = 1/a^n
Therefore, 8^-5 is equivalent to 1/8^5, and there is no expression with a positive exponent that is equivalent to 1/8^5.
What is equivalent to 6^-2
To find an expression equivalent to 6^-2 with positive exponents only, we can use the property of negative exponents:
a^-n = 1/a^n
Applying this property to the expression 6^-2, we can rewrite it as:
1/6^2
Simplifying further, we have:
1/6^2 = 1/36
Therefore, 6^-2 is equivalent to 1/36.
13^-5•13^-11
To rewrite the expression 13^-5 • 13^-11 with positive exponents only, we can apply the property of negative exponents, which states:
a^-m = 1/a^m
Let's simplify the expression step by step:
13^-5 • 13^-11 = 1/13^5 • 1/13^11
Next, we can apply the rule for multiplying fractions:
1/13^5 • 1/13^11 = 1 / (13^5 • 13^11)
Using the rule for multiplying with the same base, we can add the exponents:
13^5 • 13^11 = 13^(5+11) = 13^16
Therefore, 13^-5 • 13^-11 is equivalent to 1/13^16.