Apply the Properties of Integer Exponents to generate equivalent expressions to 4^0 ⋅ 5^−2/(−2)^−3 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with NO remaining exponents.(1 point)
4^0 ⋅ 5^−2/(−2)^−3=
Using the properties of integer exponents, we can simplify the expression:
4^0 ⋅ 5^−2/(−2)^−3 = (1 ⋅ 1)/(1/(-2)^3) = 1/(1/(-8)) = 1/(-1/8) = -8.
So, the simplified fraction is -8.
no
I apologize for the mistake. Let's correct it:
Using the rule that any number raised to the power of 0 is equal to 1, we can rewrite 4^0 as 1.
Also, using the property that a negative exponent is equal to the reciprocal of the base raised to the positive exponent, we can rewrite 5^-2 as 1/5^2 and (-2)^-3 as 1/(-2)^3.
So, the expression becomes:
1 ⋅ 1/5^2 / 1/(-2)^3
Simplifying further:
1 ⋅ 1/25 / 1/(-8)
Multiplying by the reciprocal:
1 ⋅ 1/25 * (-8/1)
Simplifying:
-8/25
Thus, the expression simplifies to -8/25.
Apply the Properties of Integer Exponents to generate equivalent expressions to (14^3⋅27^−7)^0/3^4 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
(14^3⋅27^−7)^0/3^4=
To generate equivalent expressions with positive exponents, we can use the properties of integer exponents:
(14^3⋅27^−7)^0/3^4
Using the property that any number raised to the power of 0 is equal to 1, we have:
1/3^4
Simplifying further:
1/81
Therefore, the expression (14^3⋅27^−7)^0/3^4 simplifies to 1/81.
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.(1 point)
(4^3 ⋅ 7^−2)^−5/7^9 ⋅ 4^−13=
To generate equivalent expressions with positive exponents, we can use the properties of integer exponents:
(4^3 ⋅ 7^−2)^−5/7^9 ⋅ 4^−13
Using the property that a negative exponent is equal to the reciprocal of the base raised to the positive exponent, we have:
(4^3 ⋅ 1/7^2)^−5/7^9 ⋅ 1/4^13
Simplifying further:
(64 ⋅ 1/49)^−5/7^9 ⋅ 1/4^13
Using the property that (a ⋅ b)^n = a^n ⋅ b^n, we have:
(64^−5 ⋅ (1/49)^−5)/7^45 ⋅ 1/4^13
Since any number raised to the power of -n is equal to the reciprocal of the number raised to the power of n, we have:
(1/64^5 ⋅ 49^5)/7^45 ⋅ 1/4^13
Simplifying further:
(1/ 1024^5 ⋅ 49^5)/7^45 ⋅ 1/4^13
Using the property that (a/b)^n = a^n / b^n, we have:
1/( 1024^5 ⋅ 49^5 ⋅ 7^45) ⋅ 1/4^13
Finally, simplifying the exponents and multiplying, we get:
1/(1099511627776 ⋅ 5764801 ⋅ 4639381046098370177059) ⋅ 1/268435456
Therefore, the simplified fraction with no remaining exponents for the expression (4^3 ⋅ 7^−2)^−5/7^9 ⋅ 4^−13 is 1/(2940249745775886146054600706044822145431157550401 ⋅ 268435456), which cannot be further reduced.
simple it
I apologize for the previous complex response. Let's simplify the expression:
(4^3 ⋅ 7^−2)^−5/7^9 ⋅ 4^−13
Using the property (a^m)^n = a^(m * n), we can simplify the exponents:
4^(3 * -5) ⋅ 7^(-2 * -5) / 7^(9 * -5) ⋅ 4^(-13)
Simplifying further:
4^(-15) ⋅ 7^10 / 7^(-45) ⋅ 4^(-13)
Using the property a^(-n) = 1/a^n, we have:
1/4^15 ⋅ 7^10 / 1/7^45 ⋅ 4^13
Simplifying further:
1/4^15 ⋅ 7^10 ⋅ 7^45 ⋅ 4^13
Using the property a⋅1/a = 1, we have:
1/4^15 ⋅ 7^(10 + 45) ⋅ 4^13
Simplifying the exponents:
1/4^15 ⋅ 7^55 ⋅ 4^13
Using the property (a^m)⋅(a^n) = a^(m + n), we have:
1/4^(15 + 13) ⋅ 7^55
Simplifying the exponents:
1/4^28 ⋅ 7^55
Therefore, the simplified expression is 1 / (4^28 ⋅ 7^55), which cannot be further reduced.