To apply the properties of integer exponents, we need to follow these rules:
1) To raise a power to another power, we multiply the exponents: (a^m)^n = a^(m*n).
2) To multiply two powers with the same base, we add the exponents: a^m * a^n = a^(m+n).
3) To divide two powers with the same base, we subtract the exponents: a^m / a^n = a^(m-n).
Using these rules, let's simplify the expression:
(4^3 * 7^(-2))^(-5) / (7^9 * 4^(-13))
Step 1: Simplify within the parentheses:
4^3 = 64
7^(-2) = 1/7^2 = 1/49
So, the expression becomes:
(64 * 1/49)^(-5) / (7^9 * 4^(-13))
Step 2: Combine similar exponents:
64^(-5) = (2^6)^(-5) = 2^(-30) = 1/2^30
1/49^(-5) = (7^(-2))^(-5) = 7^10 = 282,475,249
So, the expression becomes:
(1/2^30) / (7^9 * 4^(-13))
Step 3: Simplify each term:
2^30 = 1024, since 2^10 = 1024
4^(-13) = (2^2)^(-13) = 2^(-26) = 1/2^26
So, our expression becomes:
(1/2^30) / (7^9 * 1/2^26)
= 1/(2^30 * 7^9 * 1/2^26)
= 1/(2^(30-26) * 7^9)
= 1/(2^4 * 7^9)
= 1/(16 * 7^9)
= 1/(112 * 7^8)
= 1/112 * 1/(7^8)
= 1/112 * (1/7)^8
= 1/112 * (1/49)^4
= 1/112 * (1/2401)^2
= 1/112 * 1/5764801
= 1/646,835,712
Therefore, the simplified fraction without remaining exponents is 1/646,835,712.
Apply the Properties of Integer Exponents to generate equivalent expressions to (4^3x7^-2)^-5/7^9x4^-13
with only positive
exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.
(1 point)
3 answers
Wrong.
I apologize for the mistake. Let's correct the solution.
The expression is as follows:
(4^3 * 7^-2)^(-5) / (7^9 * 4^-13)
Applying the properties of integer exponents:
Step 1: Simplify within the parentheses:
4^3 = 64
7^-2 = 1/7^2 = 1/49
The expression becomes:
(64 * 1/49)^(-5) / (7^9 * 4^-13)
Step 2: Combine similar exponents:
64^-5 = (2^6)^-5 = 2^-30 = 1/2^30
1/49^-5 = (1/7^2)^-5 = (1/7^(-2 * -5)) = (1/7^10) = 1/282,475,249
The expression becomes:
(1/2^30) / (7^9 * 4^-13)
= (1/2^30) / (7^9 * (2^2)^-13)
= (1/2^30) / (7^9 * 2^-26)
= (1/2^30) / (7^9 / 2^26)
Step 3: Divide by a fraction by multiplying by the reciprocal:
(1/2^30) * (2^26 / 7^9)
= (2^26 / 2^30) * (1 / 7^9)
= 2^(26-30) / (7^9)
= 1 / (7^9)
= 1 / 403,536,070,000
Therefore, the simplified fraction without remaining exponents is 1 / 403,536,070,000.
The expression is as follows:
(4^3 * 7^-2)^(-5) / (7^9 * 4^-13)
Applying the properties of integer exponents:
Step 1: Simplify within the parentheses:
4^3 = 64
7^-2 = 1/7^2 = 1/49
The expression becomes:
(64 * 1/49)^(-5) / (7^9 * 4^-13)
Step 2: Combine similar exponents:
64^-5 = (2^6)^-5 = 2^-30 = 1/2^30
1/49^-5 = (1/7^2)^-5 = (1/7^(-2 * -5)) = (1/7^10) = 1/282,475,249
The expression becomes:
(1/2^30) / (7^9 * 4^-13)
= (1/2^30) / (7^9 * (2^2)^-13)
= (1/2^30) / (7^9 * 2^-26)
= (1/2^30) / (7^9 / 2^26)
Step 3: Divide by a fraction by multiplying by the reciprocal:
(1/2^30) * (2^26 / 7^9)
= (2^26 / 2^30) * (1 / 7^9)
= 2^(26-30) / (7^9)
= 1 / (7^9)
= 1 / 403,536,070,000
Therefore, the simplified fraction without remaining exponents is 1 / 403,536,070,000.