apply the properties of integer exponents to generate equivalent expressions to (4^(3)*7^(-2)^(-5)/(7^(9*4^(13) with only positive exponents then solve the expression your answer will be a simplified fraction with no remaining exponents
To simplify the expression, we can apply the properties of integer exponents:
1) (a^m)*(a^n) = a^(m+n)
2) a^-n = 1/a^n
3) a^0 = 1
4) (a^n)^m = a^(n*m)
Given expression: (4^(3)*7^(-2))^(-5)/(7^(9*4^13))
First, simplify the exponents inside the parentheses:
(4^3*7^(-2))^(-5)
= (64*1/49)^(-5)
= (64/49)^(-5)
= (64/49)^(-5)
Now apply the property (a^m)*(a^n) = a^(m+n) to combine the bases:
(64/49)^(-5)
= (64/49)^(-5)
= 64^(-5)/49^(-5)
Now simplify the expression by applying the property a^-n = 1/a^n:
= 1/(64^5)/(49^5)
= 1/(1073741824)/(5978711804264624)
= 1/1461501637330902918203684832716283019655932542976
= 1/1461501637330902918203684832716283019655932542976
Therefore, the simplified expression is 1/1461501637330902918203684832716283019655932542976.
wrong
To simplify the expression given, apply the properties of integer exponents:
1. (a^m)*(a^n) = a^(m+n)
2. a^-n = 1/a^n
3. (a/b)^n = a^n / b^n
Given expression: (4^3 * 7^(-2))^(-5) / 7^(9*4^13)
First simplify the exponents inside the parentheses:
(4^3 * 7^(-2))^(-5)
= (64 * (1/49))^(-5)
= (64/49)^(-5)
= 64^(-5) / 49^(-5)
= (1/64^5) / (1/49^5)
= (1/1024) / (1/59049)
= 59049 / 1024
Now we need to simplify 7^(9*4^13):
7^(9*4^13)
= 7^(9*2^26)
= 7^(2^26 * 9)
= 7^(2^26 * 3^2)
= 7^(2^26 * 3 * 3)
= 7^(2^26 * 9)
To simplify the final expression, we need to convert 7^(2^26 * 9) back to regular notation:
7^(2^26 * 9)
= 7^((2^13) * 9)
= 7^(8192 * 9)
= 7^73728
Therefore, the simplified expression is 59049 / 1024 / 7^73728.