Evaluate the expression 6^-2 x 4^0.

a)12
b)48
c)1/36
d)36

Write 3^2 x 3^-3 x 3^6 as a single exponent.

a)3^4
b)3^5
c)3^11
d)27^5

To evaluate the expression 6^-2 x 4^0, we can start by simplifying each exponent.

Since 6^-2 means 1/(6^2), we can rewrite it as 1/(6^2) = 1/36.

Since 4^0 means anything raised to the power of 0 is equal to 1, we can rewrite it as 4^0 = 1.

Now, we can substitute these values back into the expression:

1/36 x 1 = 1/36.

So, the value of the expression 6^-2 x 4^0 is c) 1/36.

Now let's simplify the expression 3^2 x 3^-3 x 3^6 as a single exponent.

When we multiply terms with the same base, we add the exponents. Therefore, we can rewrite the expression as:

3^(2+(-3)+6) = 3^(2-3+6) = 3^5.

So, the expression 3^2 x 3^-3 x 3^6 simplifies to b) 3^5.

To evaluate the expression 6^-2 x 4^0, we need to understand the properties of exponents.

First, let's rewrite the expression using these properties:

6^-2 x 4^0 = (1/6^2) x 1

Here's what we did:
- Since a negative exponent indicates taking the reciprocal of a number, we wrote 6^-2 as (1/6^2).
- Any number raised to the power of 0 is always 1, so we replaced 4^0 with 1.

Next, let's simplify the expression:

(1/6^2) x 1 = 1/36

Therefore, the answer is c) 1/36.

Now, let's simplify the expression 3^2 x 3^-3 x 3^6 as a single exponent.

To simplify this, we'll again use the properties of exponents. When multiplying two exponents with the same base, we can add their exponents:

3^2 x 3^-3 x 3^6 = 3^(2 + -3 + 6) = 3^5

Therefore, the answer is b) 3^5.

Online, “*” is used to indicate multiplication to avoid confusion with “x” as an unknown.

Please only post your questions once. Repeating posts will not get a quicker response. In addition, it wastes our time looking over reposts that have already been answered in another post. Thank you.

See your later post for the answer to the first problem.

When multiplying with exponents, you add their values.

3^2 * 3^-3 * 3^6 = 3^5