Use the Product Rule of Exponents to simplify 510⋅55 (1 point)
Responses
550
5 superscript 50 baseline
2550
25 superscript 50 baseline
2515
25 superscript 15 baseline
515
2550
Find the numerical equivalent of 99⋅9−6 . Your answer should be written without exponents.
99⋅9−6 can be simplified using the Product Rule of Exponents.
The Product Rule states that when you multiply two numbers with the same base, you add the exponents.
So, 99⋅9−6 can be rewritten as 99^(1+(-6)) = 99^(-5).
To find the numerical equivalent without exponents, we can calculate the reciprocal of 99^5.
Reciprocal of 99^5 = 1 / (99^5) ≈ 0.0000000175 (rounded to 10 decimal places)
Find the numerical equivalent of 9^9⋅9^−6 . Your answer should be written without exponents.
To simplify 9^9⋅9^−6, we will again use the Product Rule of Exponents which states that when you multiply two numbers with the same base, you add the exponents.
So, 9^9⋅9^−6 can be simplified to 9^(9+(-6)) = 9^3.
To find the numerical equivalent without exponents, we can calculate 9^3.
9^3 = 9 × 9 × 9 = 729
Therefore, the numerical equivalent of 9^9⋅9^−6 is 729.
What is the missing exponent in the following equation?
h450/h? = h^215 (1 point)
To find the missing exponent in the equation h^450/h^? = h^215, we can use the Quotient Rule of Exponents.
The Quotient Rule states that when you divide two numbers with the same base, you subtract the exponents.
So, in this equation, we have h^450/h^? = h^215. This means that the exponent in the denominator must be subtracted from the exponent in the numerator, resulting in h^450/h^? = h^(450-?).
Now, we can equate the exponent in the equation to the right side of the equation, which is h^215. Therefore, 450 - ? = 215.
Solving for ?, we subtract 215 from both sides: -? = -235.
Finally, dividing both sides by -1 to isolate ?, we find that ? = 235.
Therefore, the missing exponent in the equation is 235.
Simplify 12^87÷12^25 .(1 point)
To simplify 12^87 ÷ 12^25, we can use the Quotient Rule of Exponents, which states that when dividing two numbers with the same base, we subtract the exponents.
So, in this case, we have 12^87 ÷ 12^25.
Using the Quotient Rule, we subtract the exponent in the denominator from the exponent in the numerator: 87 - 25 = 62.
Therefore, 12^87 ÷ 12^25 simplifies to 12^62.