Question

Use the Product Rule of Exponents to simplify 5^10 ⋅ 5^5 (1 point)
Answer
Find the numerical equivalent of 9^9 ⋅ 9^−6 .(1 point)

Answer
What is the missing exponent in the following equation? h450/h? = h215 (1 point)

Answer
Simplify 12^87÷12^25 .(1 point)
Answer
What is the missing number in this simplified exponential expression: 7^?÷7^5=7^12 ?(1 point)
Answer
What is the value of 6.9−2^0 ?(1 point)
Answer
Apply the Zero Power Rule to create an equivalent expression to 9⋅(−33)^0+3/2(8−27^0) .(2 points)
Apply the Zero Power Rule to create an equivalent expression to 9⋅(−33)^0+3/2(8−27^0) .(2 points)
Answered by GPT 3.5
Using the Product Rule of Exponents, we can simplify this expression as:

5^10 ⋅ 5^5 = 5^(10+5) = 5^15
Answered by GPT 3.5
To find the numerical equivalent of the expression 9^9 ⋅ 9^−6, we can simplify it as follows:

9^9 ⋅ 9^−6 = 9^(9 + (-6)) = 9^3.

Using the rule of exponents, a^(-n) = 1/a^n, we can rewrite 9^3 as:

9^3 = (1/9^-3) = 1/((1/9^3)) = 1/(1/729) = 729.

Therefore, the numerical equivalent of 9^9 ⋅ 9^−6 is 729.
Answered by GPT 3.5
To find the missing exponent in the equation h450/h = h^215, we can use the quotient rule of exponents. According to the quotient rule, when dividing two terms with the same base, we subtract the exponents.

In this case, the base is h. So, h450/h can be rewritten as h^(450-1) = h^449.

Therefore, the missing exponent in the equation h450/h = h215 is 449.
Answered by GPT 3.5
To simplify 12^87 ÷ 12^25, we can use the quotient rule of exponents. According to the quotient rule, when dividing two terms with the same base, we subtract the exponents.

In this case, the base is 12. So, we can rewrite the expression as:

12^(87-25) = 12^62.

Therefore, the simplified form of 12^87 ÷ 12^25 is 12^62.
Answered by GPT 3.5
To find the missing number in the simplified exponential expression, we can use the quotient rule of exponents. According to the quotient rule, when dividing two terms with the same base, we subtract the exponents.

In this case, the base is 7. So, we can rewrite the expression as:

7^(?-5) = 7^12.

To isolate the missing number, we can rearrange the equation:

?-5 = 12.

Adding 5 to both sides of the equation, we get:

? = 12 + 5 = 17.

Therefore, the missing number in the simplified exponential expression is 17.
Answered by GPT 3.5
To find the value of 6.9−2^0, we can first evaluate the exponent, 2^0, which is equal to 1.

Now, the expression becomes:

6.9 - 1

Therefore, the value of 6.9−2^0 is 5.9.
Answered by GPT 3.5
To apply the Zero Power Rule and create an equivalent expression to 9 ⋅ (−33)^0 + 3/2(8 − 27^0), we need to evaluate any exponents of 0.

According to the Zero Power Rule, any non-zero number raised to the power of 0 is equal to 1.

Therefore, we can simplify the expression as:

9 ⋅ 1 + 3/2(8 - 1)

Simplifying further:

9 + 3/2(7)

Finally, we can multiply 3/2 by 7:

9 + 21/2

So, the equivalent expression is:

9 + 10.5 or 19.5