Apply the Properties of Integer Exponents to generate equivalent expressions to 222−4 with only positive exponents, then solve the expression. Provide the solution as a whole number.(1 point)
the answer is 7/16 btw
chicolloto is right !!!!! 100%
We can rewrite the expression 2^2 * 2^-4 as follows using the properties of integer exponents:
2^2 * 2^-4 = 2^(2 + -4) = 2^-2
Now, using the property a^(-n) = 1 / a^n, we can rewrite the expression as:
2^-2 = 1 / 2^2
Simplifying further:
1 / 2^2 = 1 / 4
So, the expression 2^2 * 2^-4 is equivalent to 1/4.
think again
Apologies for the previous mistake. Let's approach the problem again.
We want to rewrite the expression 2^2 * 2^-4 with only positive exponents.
Using the property of exponents a^m * a^n = a^(m + n), we can simplify the expression as follows:
2^2 * 2^-4 = 2^(2 + -4) = 2^-2
Now, let's use the property of exponents a^(-n) = 1 / a^n to rewrite the expression with a positive exponent:
2^-2 = 1/2^2
Simplifying further:
1/2^2 = 1/4
So, the expression 2^2 * 2^-4 is equivalent to 1/4.
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)
My mistake apologies for the confusion
No problem, let's try again.
To generate equivalent expressions to 2^2/2^(-4) with only positive exponents, we can use the property of exponents a^m / a^n = a^(m - n):
2^2 / 2^(-4) = 2^(2 - (-4))
Using the property of subtraction with negative numbers, we can rewrite the expression as:
2^(2 + 4) = 2^6
Now, let's solve the expression by evaluating 2^6:
2^6 = 2 * 2 * 2 * 2 * 2 * 2 = 64
So, the solution to the expression 2^2/2^(-4) is 64.
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)
To generate equivalent expressions to 4^0 ⋅ 5^(-2) / (-2)^(-3) with only positive exponents, we can apply the property of exponents a^0 = 1 and the property of negative exponents a^(-n) = 1/a^n:
1) 4^0 ⋅ 5^(-2) / (-2)^(-3)
Since any number raised to the power of 0 is equal to 1, we can rewrite this as:
2) 1 ⋅ 5^(-2) / (-2)^(-3)
Using the property of negative exponents, we can rewrite 5^(-2) as 1/5^2 and (-2)^(-3) as 1/(-2)^3:
3) 1 ⋅ 1/5^2 / 1/(-2)^3
Using the property of division with fractions, dividing by a fraction is equivalent to multiplying by its reciprocal. So, we can rewrite the expression as:
4) 1 ⋅ 1/5^2 * (-2)^3 / 1
Simplifying further:
5^2 = 25 and (-2)^3 = -2 * -2 * -2 = -8, so we have:
5) 1 ⋅ 1/25 * (-8) / 1
Multiplying the numerator and denominator:
6) -8/25
So, the given 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)
To generate equivalent expressions to (14^3⋅27^−7)^0/3^4 with only positive exponents, we can apply the property of exponents (a^m)^n = a^(m*n) and the property of negative exponents a^(-n) = 1/a^n:
1) (14^3⋅27^−7)^0/3^4
Since any number raised to the power of 0 is equal to 1, we can rewrite this as:
2) 1^0/3^4
Any number raised to the power of 0 is equal to 1, so 1^0 is also equal to 1:
3) 1/3^4
Simplifying further, 3^4 = 3 * 3 * 3 * 3 = 81:
4) 1/81
So, the given expression 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)
To generate equivalent expressions to (4^3 ⋅ 7^−2)^−5/7^9 ⋅ 4^−13 with only positive exponents, we can apply the property of exponents (a^m)^n = a^(m*n) and the property of negative exponents a^(-n) = 1/a^n:
I will simplify this expression step by step:
1) (4^3 ⋅ 7^−2)^−5/7^9 ⋅ 4^−13
Using the property of negative exponents, we can rewrite 7^(-2) as 1/7^2:
2) (4^3 ⋅ 1/7^2)^−5/7^9 ⋅ 4^−13
Next, we can simplify the expression within parentheses by evaluating the exponent of 3 for 4^3:
3) (64 ⋅ 1/7^2)^−5/7^9 ⋅ 4^−13
Simplifying inside the parentheses, we have:
4) (64/49)^−5/7^9 ⋅ 4^−13
Now, we can simplify the entire expression by evaluating the exponents.
Using the property (a/b)^n = a^n / b^n, we raise both the numerator and denominator of (64/49) to the power of -5:
5) (64^(-5)/49^(-5))/7^9 ⋅ 4^(-13)
Simplifying the exponents by applying the property of negative exponents, we have:
6) (49^5/64^5)/7^9 ⋅ 4^(-13)
Simplifying further, we have:
7) 49^5/64^5/7^9 ⋅ 4^(-13)
We can simplify 4^(-13) as 1/4^13, so the expression becomes:
8) 49^5/64^5/7^9 ⋅ 1/4^13
Now, we can simplify further by multiplying the numerators and denominators together:
9) 49^5/64^5 * 1/7^9 * 1/4^13
We can simplify the fractions by expanding the exponents:
10) 49^5/7^10 * 1/4^5 * 1/7^9 * 1/4^13
Simplifying the exponents and multiplying the fractions:
11) 49^5/7^19 * 1/4^18
We can further simplify by evaluating the value of 49^5, which is 7737809375:
12) 7737809375/7^19 * 1/4^18
Finally, we can simplify the expression by evaluating the exponents of 7^19 and 4^18:
13) 7737809375/1024 * 1/7^19
So, the simplified expression is: 7737809375/1024 * 1/7^19
are you sure?
Apologies for the mistake. Let's reevaluate the expression.
To generate equivalent expressions and solve the expression (4^3 ⋅ 7^−2)^−5/7^9 ⋅ 4^−13 with only positive exponents:
1) (4^3 ⋅ 7^−2)^−5/7^9 ⋅ 4^−13
Using the property of negative exponents, we can rewrite 7^(-2) as 1/7^2:
2) (4^3 ⋅ 1/7^2)^−5/7^9 ⋅ 4^−13
Next, we can simplify the expression within parentheses:
3) (64 ⋅ 1/49)^−5/7^9 ⋅ 4^−13
Simplifying further by evaluating the exponent of 3 for 4^3:
4) (64/49)^−5/7^9 ⋅ 4^−13
Using the property of negative exponents, we can rewrite (64/49)^(-5) as (49/64)^5:
5) (49/64)^5/7^9 ⋅ 4^−13
Now, let's evaluate the exponent of 5 for (49/64)^5:
6) (49^5/64^5)/7^9 ⋅ 4^−13
Simplifying further, we have:
7) 49^5/64^5/7^9 ⋅ 4^−13
We can simplify 4^(-13) as 1/4^13, so the expression becomes:
8) 49^5/64^5/7^9 ⋅ 1/4^13
Now, let's evaluate the exponents by expanding the values:
9) 49^5/64^5/7^9 ⋅ 1/16384
Simplifying further by calculating the values of 49^5 and 64^5:
10) 47045881/1099511627776/7^9 ⋅ 1/16384
Now, let's evaluate the exponent of 9 for 7^9:
11) 47045881/1099511627776/40353607 ⋅ 1/16384
Dividing 47045881 by 1099511627776:
12) 0.0000427847/40353607 ⋅ 1/16384
Now, let's evaluate the values:
13) 4.27847 x 10^(-8)/40353607 ⋅ 1/16384
Dividing 4.27847 x 10^(-8) by 40353607:
14) 1.06021574 x 10^(-16)/16384
Now, let's divide by 16384:
15) 6.47115 x 10^(-22)
So, the simplified expression is 6.47115 x 10^(-22).
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
(43 ⋅ 7−2)−579 ⋅ 4−13=
To generate equivalent expressions and solve the expression (4^3 ⋅ 7^−2)^−5 / 7^9 ⋅ 4^−13 with only positive exponents, we'll simplify each part of the expression separately:
1) (4^3 ⋅ 7^−2)^−5 / 7^9 ⋅ 4^−13
First, let's simplify the part inside the parentheses:
2) (64 ⋅ 1/49)^−5 / 7^9 ⋅ 4^−13
Simplifying the numerator and denominator inside the parentheses:
3) (64/49)^−5 / 7^9 ⋅ 4^−13
Now, apply the negative exponent property to rewrite (64/49)⁻⁵ as (49/64)⁵:
4) (49/64)^5 / 7^9 ⋅ 4^−13
Next, let's evaluate the exponent of 5 for (49/64)^5:
5) (49^5 / 64^5) / 7^9 ⋅ 4^−13
Now, simplify the expression further by evaluating the exponents:
6) (117649 / 1024) / 7^9 ⋅ 4^−13
Simplify 7^9 to its value:
7) (117649 / 1024) / 40353607 ⋅ 4^−13
And simplify 4^−13:
8) (117649 / 1024) / 40353607 ⋅ 1 / 4^13
Since 1 / 4^13 is equivalent to 4^-13, we have:
9) (117649 / 1024) / 40353607 ⋅ 1 / (1 / 4^13)
Simplify (1 / (1 / 4^13)) as (1 * 4^13):
10) (117649 / 1024) / 40353607 ⋅ 4^13
Evaluate 4^13:
11) (117649 / 1024) / 40353607 ⋅ 67108864
And simplify (117649 / 1024) / 40353607:
12) 117649 / (1024 * 40353607) ⋅ 67108864
Multiply 1024 and 40353607:
13) 117649 / 41426549568 ⋅ 67108864
Evaluate 41426549568 * 67108864:
14) 117649 / 2772004491078283776
So, the simplified expression is 117649 / 2772004491078283776.
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
(4^3 ⋅ 7^−2)^−5 / 7^9 ⋅ 4^−13=
To simplify the expression (4^3 ⋅ 7^−2)^−5 / 7^9 ⋅ 4^−13 with only positive exponents, let's break it down into smaller steps:
1) Begin by simplifying the numerator inside the parentheses:
(4^3 ⋅ 7^−2)^−5 = (64 ⋅ 1/49)^−5
2) Apply the property of negative exponents to the numerator:
(64 ⋅ 1/49)^−5 = (64/49)^−5
3) Apply the negative exponent to the base:
(64/49)^−5 = (49/64)^5
4) Simplify the denominator:
7^9 = 7^(3 x 3) = (7^3)^3 = 343^3
5) Simplify the second part of the expression:
4^−13 = 1/4^13
6) Substitute the simplified forms back into the expression:
((49/64)^5) / (343^3) ⋅ (1/4^13)
7) Simplify the numerator:
(49^5 / 64^5) / (343^3) ⋅ (1/4^13)
8) Simplify the denominator:
(49^5 / 64^5) / (343^3) ⋅ (1/2^26)
9) Simplify the fraction in the numerator:
49^5 / 64^5 = (7^2)^5 / (2^6)^5 = 7^10 / 2^30
10) Substitute the simplified forms back into the expression:
(7^10 / 2^30) / (343^3) ⋅ (1/2^26)
11) Simplify the denominator:
(7^10 / 2^30) / (7^3)^3 ⋅ (1/2^26) = 7^10 / 7^9 ⋅ (1/2^26)
12) Simplify further:
7^10 / 7^9 = 7^(10-9) = 7^1 = 7
13) Substitute the simplified forms back into the expression:
7 / (1/2^26)
14) Simplify the reciprocal in the denominator:
7 / (1/2^26) = 7 * 2^26 = 7 * (2^13)^2 = 7 * 8192^2 = 7 * 67108864 = 469762048
So, the simplified expression is 469762048.
(4^3 ⋅ 7^−2)^−5
To simplify the expression (4^3 ⋅ 7^−2)^−5, we can follow these steps:
1) Begin by simplifying the numerator inside the parentheses:
(4^3 ⋅ 7^−2)^−5
2) Evaluate 4^3 and 7^−2:
64 ⋅ 1/49
3) Combine the terms in the numerator:
64/49
4) Apply the negative exponent to the fraction:
(64/49)^−5
5) To apply the negative exponent, we take the reciprocal of the fraction and change the