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.