Apply the Property of Negative Integer Exponents to generate an expression equivalent to 3−178−14 with positive exponents only.(1 point)
3−178−14=
3^-17 * 8^-14
answer?
The expression with positive exponents only is (1/3^17) * (1/8^14).
ANSWER JUST SAY THE ANSWER NOTHING ELSE
(1/3^17) * (1/8^14)
Apply the Properties of Integer Exponents to generate equivalent expressions to (7−3)7 ⋅ 7206−2 with only positive exponents, then solve the expression. Provide the answer as an improper fraction.(1 point)
(7−3)7 ⋅ 7206−2=
(7^-3)(7^7) * (720^6)^-2
Apply the product rule of integer exponents to find the numerical equivalent of 12−5⋅127. Show your work and explain how you used the product rule of integer exponents.(2 points)
To apply the Property of Negative Integer Exponents, we use the following rule:
For any non-zero number a, and any positive integers m and n:
a^(-m) = 1 / a^m
Now let's apply this property to generate an expression equivalent to 3^(-17) * 8^(-14) with only positive exponents.
First, let's take care of 3^(-17). According to the rule, we need to rewrite it as 1 / 3^17.
Similarly, for 8^(-14), we rewrite it as 1 / 8^14.
Therefore, the expression 3^(-17) * 8^(-14) is equivalent to:
1 / 3^17 * 1 / 8^14
To simplify further, we can express 8 as 2^3:
1 / (3^17 * 2^(3*14))
Now, let's simplify the expression by combining like terms:
1 / (3^17 * 2^42)
This is the equivalent expression of 3^(-17) * 8^(-14) with positive exponents only.
To find the numerical equivalent of 12^-5 * 12^7, we can use the product rule of integer exponents, which states that when multiplying two base numbers with the same exponent, we can add the exponents.
In this case, we have 12 as the base and -5 and 7 as the exponents.
Applying the product rule, we add the exponents:
12^-5 * 12^7 = 12^(-5 + 7)
Simplifying further, we get:
12^2
Hence, the numerical equivalent of 12^-5 * 12^7 is 12^2, or 144.