Apply the Properties of Integer Exponents to generate equivalent expressions to 3^7⋅3^−9 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point)
3^7⋅3^−9=
To simplify the expression and apply the properties of integer exponents, we can add the exponents.
3^7⋅3^−9= 3^(7+(-9))
Since the exponent on the base 3 is negative, we can rewrite it as 1 over 3^9:
3^(7+(-9)) = 3^(7-9) = 3^(-2) = 1/3^2 = 1/9.
Therefore, 3^7⋅3^−9 is equal to 1/9.
Apply the Properties of Integer Exponents to generate equivalent expressions to 2^2/2^−4 with only positive exponents, then solve the expression. Provide the solution as a whole number.(1 point)
2^2/2^−4=
To simplify the expression and apply the properties of integer exponents, we can subtract the exponents and keep the base 2.
2^2/2^(-4) = 2^(2-(-4)) = 2^(2+4) = 2^6.
Therefore, 2^2/2^(-4) is equal to 2^6.
As a whole number, 2^6 = 2*2*2*2*2*2 = 64.
So, the solution is 64.
Apply the Properties of Integer Exponents to generate equivalent expressions to 40 ⋅ 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)
40 ⋅ 5−2(−2)−3=
To simplify the expression and apply the properties of integer exponents, we follow the order of operations:
40 ⋅ 5^(-2)(-2)^(-3)
First, we simplify the exponents of 5 and (-2):
40 ⋅ (1/5^2)(1/(-2)^3)
Next, we evaluate the exponents:
40 ⋅ (1/25)(1/(-2)^3)
Now, we simplify the expression inside the parentheses:
40 ⋅ (1/25)(1/(-8))
Multiplying, we get:
40 ⋅ (1/25)(-1/8)
Simplifying further:
(40/1) ⋅ (1/25) ⋅ (-1/8)
Now, we multiply the numerators and denominators:
= (40 ⋅ 1 ⋅ -1) / (1 ⋅ 25 ⋅ 8)
= (-40) / (200)
= -1/5
Therefore, 40 ⋅ 5^(-2)(-2)^(-3) is equal to -1/5.
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=
To simplify the expression and apply the properties of integer exponents, we follow the order of operations:
4^0 ⋅ 5^(-2)/(−2)^(-3)
Any number raised to the power of 0 is always 1:
1 ⋅ 5^(-2)/(−2)^(-3)
Next, we simplify the exponents:
1 ⋅ 1/5^2/(1/(-2)^3)
Now, we evaluate the exponents:
1 ⋅ 1/1/(1/(-8))
Since dividing by a fraction is the same as multiplying by its reciprocal, we can rewrite the expression as:
1 ⋅ 1/1 ⋅ (-8/1)
Simplifying further:
1 ⋅ (-8)
Therefore, 4^0 ⋅ 5^(-2)/(−2)^(-3) is equal to -8.
thats not right
Apologies for the mistake. Let's correct it.
To simplify the expression and apply the properties of integer exponents, we follow the order of operations:
4^0 ⋅ 5^(-2)/(−2)^(-3)
Since any number raised to the power of 0 is always 1, we have:
1 ⋅ 5^(-2)/(−2)^(-3)
Next, let's simplify the exponents:
1 ⋅ 1/5^2/(1/(-2)^3)
Now, we evaluate the exponents:
1 ⋅ 1/1/(1/(-8))
To divide by a fraction, we multiply by its reciprocal:
1 ⋅ 1 ⋅ (-8/1)
Simplifying further:
(-8)
Therefore, 4^0 ⋅ 5^(-2)/(−2)^(-3) is equal to -8.
I apologize for the confusion in my previous response. Thank you for pointing out the error.