Question

Apply the power of a power rule to simplify the expression (8-2)^?

a) -812+3 - 915

b) -812×3

c) -836

d) (812) - 32

e) -812- 3 - gt

Answer 1

The power of a power rule entails multiplying exponents when an exponentiated number is raised to another power. Knowledge of multiplying and dividing powers of 10 is also crucial, where exponents are added for multiplication, and subtracted for division.

Step-by-step explanation:

The question 'Apply the power of a power rule to simplify the expression (8-2)?' involves using the power of a power rule which is a fundamental concept in algebra. This rule states that when raising an exponent to another power, you multiply the exponents. An example of applying the power of a power rule is (ab)c = ab × c. In the expression (8-2)?, if '?' were an integer, you would multiply -2 by that integer to obtain the new exponent of 8.

Additionally, knowledge of operations with powers of 10 is useful. When you multiply powers of 10, you add the exponents; for division, you subtract them. For example, 105 × 103 = 105+3 = 108, and 105 / 103 = 105-3 = 102.

Answer 2

c) -836

The application of the power of a power rule simplifies the expression
`(8-2)^?` to -836.

Step-by-step explanation:

Applying the power of a power rule involves multiplying the exponents. In the expression
`(8-2)^?`, the outer exponent is the question mark, and the inner exponent is the difference between 8 and 2.

`\[ (8-2)^? = 6^? \]`

To simplify further, we multiply the exponents:

`\[ 6^? = 6^1 * 6^(? - 1) = 6 * 6^(? - 1) \]`

So, the expression simplifies to -836.