Simplify the following

2^16/2^-5

3 answers

To simplify the expression, we can write it as a single fraction with the same base:

2^16 / 2^-5

First, let's move the negative exponent to the numerator by flipping the fraction:

2^16 * 2^5

Next, we can simplify the expression using the rule of exponents that states when you multiply two exponents with the same base, you add the exponents:

2^(16+5)

Adding the exponents, we get:

2^21

Therefore, the simplified expression is 2^21.
Find the missing value

x^?/x^6=x^10
To find the missing value, we need to determine what power of x would make the equation x^? / x^6 = x^10 true.

Using the property of exponentiation that states when dividing two exponents with the same base, you subtract the exponents:

x^(? - 6) = x^10

We want the exponents to be equal on both sides of the equation, so ? - 6 = 10.

To solve for ?, we add 6 to both sides of the equation:

? = 10 + 6

?= 16

Therefore, the missing value is 16.