Apply the properties of integers exponents to generate equivalent expressions to 2^2/2^-4 what only positive exponents, then solve the expression, but in a whole number
To generate an equivalent expression with only positive exponents, we can use the property of negative exponents, which states that any number raised to a negative exponent can be rewritten as the reciprocal of the number raised to the positive exponent.
Simplifying the expression 2^2/2^-4 using this property, we have:
2^2 / 2^-4
= 2^(2 + 4)
= 2^6
Now, solving the expression, we get:
2^6
= 2 × 2 × 2 × 2 × 2 × 2
= 64
So, the value of the expression 2^2/2^-4, with only positive exponents and in a whole number, is 64.
To generate an equivalent expression with only positive exponents, we can use the properties of integers exponents. Specifically, we can use the rule that states: a^(-n) is equal to 1/a^n.
So, let's apply this rule to the expression 2^2 / 2^(-4):
2^2 / 2^(-4) = 2^2 / (1/2^4)
Since 1/2^4 is the same as 2^(-4), we can rewrite the expression as:
2^2 / 2^(-4) = 2^2 / 2^(-4) = 2^2 * 2^4
Now, we can use the property that states: a^m * a^n = a^(m+n), to simplify the expression further:
2^2 * 2^4 = 2^(2+4) = 2^6
Finally, to solve the expression and obtain a whole number, we can evaluate 2^6:
2^6 = 2 * 2 * 2 * 2 * 2 * 2 = 64
Therefore, the simplified expression equals 64 as a whole number.
To generate an equivalent expression for 2^2/2^-4 with only positive exponents, you can use the properties of integer exponents.
First, let's recall the properties of exponents:
1. Product of Powers Property: (a^m) * (a^n) = a^(m + n)
2. Quotient of Powers Property: (a^m) / (a^n) = a^(m - n)
3. Power of a Power Property: (a^m)^n = a^(m * n)
4. Negative Exponent Property: a^-n = 1 / a^n
Now, let's simplify 2^2/2^-4 step by step:
Step 1: Simplify the numerator
In the numerator, we have 2^2. Applying the power rule, we get 2^2 = 2 * 2 = 4.
Step 2: Simplify the denominator
In the denominator, we have 2^-4. Using the negative exponent property, we can rewrite it as 1 / 2^4.
Step 3: Simplify the whole expression
Now we have 4 / (1 / 2^4). Using the quotient of powers property, we can rewrite it as 4 * 2^4 = 4 * 16 = 64.
Therefore, the equivalent expression to 2^2/2^-4 with only positive exponents is 64.