Question
Use the Product Rule of Exponents to simplify 5 to the power of 10 times 5 to the power of 5
(1 point)
Responses
2515
25 superscript 15 baseline
550
5 superscript 50 baseline
515
5 superscript 15 baseline
2550
(1 point)
Responses
2515
25 superscript 15 baseline
550
5 superscript 50 baseline
515
5 superscript 15 baseline
2550
Answers
Answer
Find the numerical equivalent of 9to the power of9⋅9to the power of −6
. Your answer should be written without exponents. (1 point)
. Your answer should be written without exponents. (1 point)
Answer
What is the missing exponent in the following equation?
h the power of 450 divided by h? = h215
(1 point)
h the power of 450 divided by h? = h215
(1 point)
Answer
Simplify 12 to the power of 87÷12 to the power of 25
.
.
Answer
Apply the Zero Power Rule to create an equivalent expression to 9⋅(−33)0+32(8−270)
.(2 points)
.(2 points)
Answer
Apply the Property of Negative Integer Exponents to solve 7to the power of−3
. The answer should not contain any exponent expression or decimals.(1 point)
. The answer should not contain any exponent expression or decimals.(1 point)
Answered by
GPT-4o mini
To simplify \( 5^{10} \times 5^{5} \) using the Product Rule of Exponents, you add the exponents:
\[
5^{10} \times 5^{5} = 5^{10+5} = 5^{15}
\]
So, the correct answer is:
**5 superscript 15 baseline**.
\[
5^{10} \times 5^{5} = 5^{10+5} = 5^{15}
\]
So, the correct answer is:
**5 superscript 15 baseline**.
Answered by
GPT-4o mini
To find the numerical equivalent of \( 9^9 \cdot 9^{-6} \), we can use the Product Rule of Exponents, which states that when multiplying two powers with the same base, we add the exponents:
\[
9^9 \cdot 9^{-6} = 9^{9 + (-6)} = 9^{3}
\]
Now we can calculate \( 9^3 \):
\[
9^3 = 9 \cdot 9 \cdot 9 = 81 \cdot 9 = 729
\]
Thus, the numerical equivalent is **729**.
\[
9^9 \cdot 9^{-6} = 9^{9 + (-6)} = 9^{3}
\]
Now we can calculate \( 9^3 \):
\[
9^3 = 9 \cdot 9 \cdot 9 = 81 \cdot 9 = 729
\]
Thus, the numerical equivalent is **729**.
Answered by
GPT-4o mini
To find the missing exponent in the equation
\[
\frac{h^{450}}{h^{?}} = h^{215},
\]
we can use the Quotient Rule of Exponents, which states that when dividing two powers with the same base, we subtract the exponents:
\[
\frac{h^{450}}{h^{?}} = h^{450 - ?}.
\]
We want this to equal \(h^{215}\):
\[
h^{450 - ?} = h^{215}.
\]
Setting the exponents equal to each other gives us:
\[
450 - ? = 215.
\]
Now, we can solve for the missing exponent:
\[
? = 450 - 215 = 235.
\]
Thus, the missing exponent is **235**.
\[
\frac{h^{450}}{h^{?}} = h^{215},
\]
we can use the Quotient Rule of Exponents, which states that when dividing two powers with the same base, we subtract the exponents:
\[
\frac{h^{450}}{h^{?}} = h^{450 - ?}.
\]
We want this to equal \(h^{215}\):
\[
h^{450 - ?} = h^{215}.
\]
Setting the exponents equal to each other gives us:
\[
450 - ? = 215.
\]
Now, we can solve for the missing exponent:
\[
? = 450 - 215 = 235.
\]
Thus, the missing exponent is **235**.
Answered by
GPT-4o mini
To simplify \( \frac{12^{87}}{12^{25}} \), you can use the Quotient Rule of Exponents. This rule states that when dividing two powers with the same base, you subtract the exponents:
\[
\frac{a^m}{a^n} = a^{m - n}.
\]
Applying it here:
\[
\frac{12^{87}}{12^{25}} = 12^{87 - 25} = 12^{62}.
\]
So, the simplified form is **12 to the power of 62**.
\[
\frac{a^m}{a^n} = a^{m - n}.
\]
Applying it here:
\[
\frac{12^{87}}{12^{25}} = 12^{87 - 25} = 12^{62}.
\]
So, the simplified form is **12 to the power of 62**.
Answered by
GPT-4o mini
To apply the Zero Power Rule, we need to recognize that any non-zero number raised to the power of zero equals 1. Thus, the term \((-33)^0\) can be simplified:
\[
(-33)^0 = 1.
\]
Now, substituting this back into the expression:
\[
9 \cdot (−33)^0 + 32(8 - 270).
\]
This simplifies to:
\[
9 \cdot 1 + 32(8 - 270).
\]
Now simplifying further:
\[
9 + 32(8 - 270).
\]
Next, simplify the expression inside the parentheses:
\[
8 - 270 = -262.
\]
Now substituting this back into the expression gives:
\[
9 + 32 \cdot (-262).
\]
Calculating \(32 \cdot (-262)\):
\[
32 \cdot (-262) = -8384.
\]
Now substituting this back gives:
\[
9 - 8384.
\]
Finally, calculating \(9 - 8384\):
\[
9 - 8384 = -8375.
\]
Thus, the equivalent expression is \(-8375\).
\[
(-33)^0 = 1.
\]
Now, substituting this back into the expression:
\[
9 \cdot (−33)^0 + 32(8 - 270).
\]
This simplifies to:
\[
9 \cdot 1 + 32(8 - 270).
\]
Now simplifying further:
\[
9 + 32(8 - 270).
\]
Next, simplify the expression inside the parentheses:
\[
8 - 270 = -262.
\]
Now substituting this back into the expression gives:
\[
9 + 32 \cdot (-262).
\]
Calculating \(32 \cdot (-262)\):
\[
32 \cdot (-262) = -8384.
\]
Now substituting this back gives:
\[
9 - 8384.
\]
Finally, calculating \(9 - 8384\):
\[
9 - 8384 = -8375.
\]
Thus, the equivalent expression is \(-8375\).
Answered by
GPT-4o mini
To apply the Property of Negative Integer Exponents, we use the rule that states:
\[
a^{-n} = \frac{1}{a^n}.
\]
For \(7^{-3}\), we can rewrite it as:
\[
7^{-3} = \frac{1}{7^3}.
\]
Next, we need to calculate \(7^3\):
\[
7^3 = 7 \times 7 \times 7 = 49 \times 7 = 343.
\]
Thus,
\[
7^{-3} = \frac{1}{7^3} = \frac{1}{343}.
\]
So, the final answer is:
\[
\frac{1}{343}.
\]
\[
a^{-n} = \frac{1}{a^n}.
\]
For \(7^{-3}\), we can rewrite it as:
\[
7^{-3} = \frac{1}{7^3}.
\]
Next, we need to calculate \(7^3\):
\[
7^3 = 7 \times 7 \times 7 = 49 \times 7 = 343.
\]
Thus,
\[
7^{-3} = \frac{1}{7^3} = \frac{1}{343}.
\]
So, the final answer is:
\[
\frac{1}{343}.
\]