When you are multiplying and the bases are the same, you add the exponents together. Because both bases are you add as your new exponent. You then keep the same base, , to the 7th power.

Apply the the various properties of exponents:

(x3y6z)(x2yz3)

The paraentheses are irrelevant. Rearrange to combine like terms.

x3x2y6y1z1z3

When you multiply variables with exponents, simply add the exponents together.

x3+2 y6+1 z1+3

x5y7z4

The question tells us that 22_a_ ( 22_b_ )= 16.

We can rewrite 16 as 24, giving us 22_a_ ( 22_b_ )= 24.

When terms with the same base are multipled, their exponents can be added:

2(2_a_ +2_b_) = 24

Since the base is the same on both sides of the equation, we can equate the exponents:

2_a_ +2_b_ = 4

2(a + b) = 4

a + b = 2

1. Solve for x in 3x = 27. x = 3 because 3 * 3 * 3 = 27.
2. Since x = 3, one can substitute x for 3 in 22x
3. Now, the expression is 22*3
4. This expression can be interpreted as 22 * 22 * 22. Since 22 = 4, the expression can be simplified to become 4 * 4 * 4 = 64.
5. You can also multiply the powers to simplify the expression. When you multiply the powers, you get 26, or 2 * 2 * 2 * 2 * 2 * 2
6. 26 = 64.

The three two multiply to become 8 and the powers of ten can be added to become 1021.

In order to solve this equation, we first need to find a common base for the exponents. We know that 23 = 8 and 24 = 16, so it makes sense to use 2 as a common base, and then rewrite each side of the equation as a power of 2.

8x-3 = (23)x-3

We need to remember our property of exponents which says that (ab)c = abc.

Thus (23)x-3 = 23(x-3) = 23x - 9.

We can do the same thing with 164-x.

164-x = (24)4-x = 24(4-x) = 216-4x.

So now our equation becomes

23x - 9 = 216-4x

In order to solve this equation, the exponents have to be equal.

3x - 9 = 16 - 4x

Add 4x to both sides.

7x - 9 = 16

Add 9 to both sides.

7x = 25

Divide by 7.

x = 25/7.

We can start by rewriting 411 as 4 * 410. This will allow us to collect the like terms 410 into a single term.

410 + 410 + 410 + 410 + 411

= 410 + 410 + 410 + 410 + 4 * 410

= 8 * 410

Because the answer choices are written with a base of 2, we need to rewrite 8 and 4 using bases of two. Remember that 8 = 23, and 4 = 22.

8 * 410

= (23)(22)10

We also need to use the property of exponents that (ab)c = abc. We can rewrite (22)10 as 22x10 = 220.

(23)(22)10

= (23)(220)

Finally, we must use the property of exponents that ab * ac = ab+c.

(23)(220) = 223

The answer is 223.

and can be multiplied together to give you which is the first part of our answer. When you multiply exponents with the same base (in this case, ), you add the exponents. In this case, should give us because . The answer is