Simplify 5^10 . 5^5

5 answers

To simplify 5^10 * 5^5, you can add the exponents since the bases are the same:

5^(10+5) = 5^15

Therefore, 5^10 * 5^5 simplifies to 5^15.
What is a numerical equivalent to 9^9 . 9^-6
To simplify 9^9 * 9^(-6), you can subtract the exponents since the bases are the same:

9^(9-6) = 9^3

Therefore, 9^9 * 9^(-6) simplifies to 9^3.
Apply the Zero Power Rule to create an equivalent expression to 9⋅(−33)^0+3/2(8−2/7^0) .(2 points)
The Zero Power Rule states that any non-zero number raised to the power of zero is equal to 1. Therefore, applying the Zero Power Rule, the expression (-33)^0 simplifies to 1.

Using this rule, we can rewrite the expression 9⋅(−33)^0+3/2(8−2/7^0) as:

9 * 1 + 3/2(8 - 1)

Simplifying further:

9 + 3/2(7)

Now, simplifying the expression inside the parenthesis:

9 + 21/2

To add the fractions, we need to find a common denominator:

9 + (21 * 2)/(2 * 2)

= 9 + 42/4

The constant 9 can be written as a fraction: 9/1

Adding the fractions:

(9 * 4 + 42)/(4)

= (36 + 42)/4

= 78/4

= 39/2

Therefore, the simplified expression is 39/2.