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 generate equivalent expressions with only positive exponents, we can use the properties of integer exponents.
First, let's simplify the expression using these properties:
2^2/2^(-4)
Using the property a^m/a^n = a^(m-n):
2^(2-(-4))
Simplifying the exponent:
2^(2+4)
Adding the exponents:
2^6
Therefore, the equivalent expression with only positive exponents is 2^6.
To solve the expression and provide the solution as a whole number, we evaluate 2^6:
2^6 = 2 × 2 × 2 × 2 × 2 × 2 = 64
Therefore, the solution as a whole number is 64.
To generate an equivalent expression with only positive exponents, we can use the properties of integer exponents.
The property we will use is:
a^m / a^n = a^(m - n)
Applying this property to the expression 2^2/2^(-4), we get:
2^2 / 2^(-4) = 2^(2 - (-4))
Simplifying the exponent, we have:
2^2 / 2^(-4) = 2^(2 + 4)
Now, we can evaluate the expression:
2^(2 + 4) = 2^6
Therefore, the equivalent expression with only positive exponents is 2^6.
Now, we can solve the expression:
2^6 = 2 * 2 * 2 * 2 * 2 * 2
Calculating this, we find that 2^6 = 64.
So, the solution as a whole number is 64.