2^-2•2^?=2^14

=?

2^-2 • 2^? = 2^14

Using the properties of exponents, we can simplify this equation:

2^-2 • 2^? = 2^14
Since the base (2) is the same on both sides, we can set the exponents equal to each other:

-2 + ? = 14

To isolate the variable, we can add 2 to both sides:

? = 14 + 2

Simplifying, we get:

? = 16

Therefore, the value of ? that makes the equation true is 16.

x^2\cdotx^?=x^11

?=

To solve for the value of ?, we can use the properties of exponents:

x^2 • x^? = x^11

When multiplying terms with the same base, we add the exponents:

x^(2 + ?) = x^11

To make the bases equal, we need the exponents to be the same. Therefore, we set 2 + ? = 11.

Solving for ?, we get:

? = 11 - 2
? = 9

Therefore, the value of ? that makes the equation true is 9.

5^8•5^?=5^15

?=

To find the value of ?, we can use the properties of exponents:

5^8 • 5^? = 5^15

When multiplying terms with the same base, we add the exponents:

5^(8 + ?) = 5^15

To make the bases equal, we need the exponents to be the same. Therefore, we set 8 + ? = 15.

Solving for ?, we get:

? = 15 - 8
? = 7

Therefore, the value of ? that makes the equation true is 7.

7^17

______
7^-2

To find the value of the expression 7^17 / 7^-2, we can use the properties of exponents:

7^17 / 7^-2

When dividing terms with the same base, we subtract the exponents:

7^(17 - (-2))

Simplifying the subtraction, we get:

7^(17 + 2)

Therefore, 7^17 / 7^-2 is equal to 7^19.

x^?

____ =x^15
x^8

To find the value of ?, we can use the properties of exponents:

(x^?) / (x^8) = x^15

When dividing terms with the same base, we subtract the exponents:

x^(? - 8) = x^15

To make the bases equal, we need the exponents to be the same. Therefore, we set ? - 8 = 15.

Solving for ?, we get:

? = 15 + 8
? = 23

Therefore, the value of ? that makes the equation true is 23.

To find the value of the question mark, we can use the properties of exponents:

First, let's simplify the left side of the equation:
2^-2 • 2^? = 2^( -2 + ? ) (using the property that when you multiply two exponents with the same base, you add the exponents)

Now we can set up an equation:
2^( -2 + ? ) = 2^14

To solve this equation, we can equate the exponents:

-2 + ? = 14

To isolate the question mark, we can add 2 to both sides:

? = 14 + 2

Therefore, the value of ? is 16.