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use the product rule of exponents to simplify 5^10 . 5^5
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Answered by
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find the numerical equivalent of 9^9 . 9^-6
9^9 . 9^-6 =
9^9 . 9^-6 =
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what is the missing exponent in the following equation?
h^450/h^? = h^215 =
h^450/h^? = h^215 =
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simplifying 12^87 divided by 12^25
12^87 divided by 12^25 =
12^87 divided by 12^25 =
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what is the missing number in this simplified exponential expression 7^2 divided by 7^5 = 7^12?
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what is the value of 6.9 - 2^0?
a 7.9
b 4.9
c 5.9
d 6.9
a 7.9
b 4.9
c 5.9
d 6.9
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apply the zero power rule to create an equivalent expression to 9 . (-33)^0 + 3/2 (8 - 27^0)
9 . (-33)^0 + 3/2 (8 - 27^0) = __ . __ + 3/2 (__ - __)
9 . (-33)^0 + 3/2 (8 - 27^0) = __ . __ + 3/2 (__ - __)
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solve the expression 15.8^0/5 + 4 (7^0 - 6)
15.8^0/5 + 4 (7^0 - 6) =
15.8^0/5 + 4 (7^0 - 6) =
Answered by
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use the power rule of exponents to simplify (10^3)^6
(10^3)^6 =
(10^3)^6 =
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use the power rule of exponents to simplify (10^3)^6
(10^3)^6 = ___
(10^3)^6 = ___
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if the expression 7^15 was simplified using the power rule of exponents, which of the following would be an expanded equiavlent expression?
a 7(18)^3
b 7(10)^5
c (7 . 7 . 7 . 7 . 7)^10
d ( 7 . 7 . 7) . ( 7 . 7 . 7) . ( 7 . 7 . 7) . ( 7 . 7 . 7) . ( 7 . 7 . 7)
a 7(18)^3
b 7(10)^5
c (7 . 7 . 7 . 7 . 7)^10
d ( 7 . 7 . 7) . ( 7 . 7 . 7) . ( 7 . 7 . 7) . ( 7 . 7 . 7) . ( 7 . 7 . 7)
Answered by
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use the power rule of exponents to create a simplified equivalent expression for (19^4)^9
(19^4)^9 = ___
(19^4)^9 = ___
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apply the property of negative integer exponents to solve 7^-3. the answer should not contain any exponent expression or decimals.
7^-3 = ___
7^-3 = ___
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apply the property of negative integer exponents to generate an expression equivalent to 3^-17/8^-14 with positive exponents only.
3^-17/8^-14 = _____
3^-17/8^-14 = _____
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apply the properties of integer exponents to generate equivalent expressions to (7^3) . 7^20/6^-2 with only positive exponents, then solve the expressions. provide the answers as an improper fraction.
(7^3) . 7^20/6^-2 = ____
(7^3) . 7^20/6^-2 = ____
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apply the product rule of integer exponents to find the numerical equivalent of 12^-5 . 12^7. show you work and explain how you used the product rule of integer exponents.
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GPT 3.5
To simplify the expression 5^10 * 5^5 using the product rule of exponents, we add the exponents together.
When multiplying two terms with the same base, we add the exponents.
Therefore, 5^10 * 5^5 = 5^(10+5) = 5^15
When multiplying two terms with the same base, we add the exponents.
Therefore, 5^10 * 5^5 = 5^(10+5) = 5^15
Answered by
GPT 3.5
To simplify the expression 9^9 * 9^-6, we can use the quotient rule of exponents.
According to the quotient rule of exponents, when dividing two terms with the same base, we subtract the exponents.
Therefore, 9^9 * 9^-6 = 9^(9-6) = 9^3.
The numerical equivalent of 9^3 is 729.
According to the quotient rule of exponents, when dividing two terms with the same base, we subtract the exponents.
Therefore, 9^9 * 9^-6 = 9^(9-6) = 9^3.
The numerical equivalent of 9^3 is 729.
Answered by
GPT 3.5
To find the missing exponent in the equation h^450/h^? = h^215, we can use the quotient rule of exponents.
According to the quotient rule of exponents, when dividing two terms with the same base, we subtract the exponents.
So, in this case, h^450 / h^? = h^215 can be rewritten as h^(450-?) = h^215.
To find the missing exponent, we set the exponents equal to each other: 450 - ? = 215.
Next, we solve for the missing exponent by subtracting 215 from both sides: 450 - 215 = ?.
Therefore, the missing exponent in the equation is ? = 235.
According to the quotient rule of exponents, when dividing two terms with the same base, we subtract the exponents.
So, in this case, h^450 / h^? = h^215 can be rewritten as h^(450-?) = h^215.
To find the missing exponent, we set the exponents equal to each other: 450 - ? = 215.
Next, we solve for the missing exponent by subtracting 215 from both sides: 450 - 215 = ?.
Therefore, the missing exponent in the equation is ? = 235.
Answered by
GPT 3.5
To simplify 12^87 divided by 12^25, we can use the quotient rule of exponents.
According to the quotient rule of exponents, when dividing two terms with the same base, we subtract the exponents.
So, in this case, 12^87 divided by 12^25 can be rewritten as 12^(87-25).
Simplifying the exponent, we have 12^62.
Therefore, 12^87 divided by 12^25 is equal to 12^62.
According to the quotient rule of exponents, when dividing two terms with the same base, we subtract the exponents.
So, in this case, 12^87 divided by 12^25 can be rewritten as 12^(87-25).
Simplifying the exponent, we have 12^62.
Therefore, 12^87 divided by 12^25 is equal to 12^62.
Answered by
GPT 3.5
To find the missing number in the simplified expression 7^2 divided by 7^5 = 7^12, we can use the quotient rule of exponents.
According to the quotient rule of exponents, when dividing two terms with the same base, we subtract the exponents.
So, in this case, we have 7^2 divided by 7^5, which can be rewritten as 7^(2-5).
Simplifying the exponent, we have 7^(-3).
Therefore, the missing number in the simplified expression is -3.
According to the quotient rule of exponents, when dividing two terms with the same base, we subtract the exponents.
So, in this case, we have 7^2 divided by 7^5, which can be rewritten as 7^(2-5).
Simplifying the exponent, we have 7^(-3).
Therefore, the missing number in the simplified expression is -3.
Answered by
GPT 3.5
The value of 6.9 - 2^0 is equal to 6.9 - 1.
Since any number raised to the power of 0 is equal to 1, we have 6.9 - 1 = 5.9.
Therefore, the correct answer is c) 5.9.
Since any number raised to the power of 0 is equal to 1, we have 6.9 - 1 = 5.9.
Therefore, the correct answer is c) 5.9.
Answered by
GPT 3.5
Applying the zero power rule, any non-zero number raised to the power of 0 is equal to 1.
Therefore, (-33)^0 = 1 and 27^0 = 1.
Using the zero power rule, we can rewrite the expression as:
9 . 1 + 3/2 (8 - 1)
Simplifying further:
9 + 3/2 (8 - 1)
So, the equivalent expression is:
9 . 1 + 3/2 (8 - 1) = 9 + 3/2 (8 - 1)
Therefore, (-33)^0 = 1 and 27^0 = 1.
Using the zero power rule, we can rewrite the expression as:
9 . 1 + 3/2 (8 - 1)
Simplifying further:
9 + 3/2 (8 - 1)
So, the equivalent expression is:
9 . 1 + 3/2 (8 - 1) = 9 + 3/2 (8 - 1)
Answered by
GPT 3.5
To solve the expression 15.8^0/5 + 4 (7^0 - 6), we first evaluate any exponents and then perform the operations from left to right according to the order of operations (PEMDAS).
Starting with the exponent 15.8^0, any number raised to the power of 0 is equal to 1. Therefore, 15.8^0 = 1.
Now we can replace the exponent in the expression:
1/5 + 4 (7^0 - 6)
Next, we evaluate 7^0, which is equal to 1.
1/5 + 4 (1 - 6)
Within the parentheses, we perform the subtraction:
1/5 + 4 (-5)
Next, we perform the multiplication:
1/5 - 20
To combine the fractions, we need to have a common denominator:
1/5 - 100/5
Now we can subtract:
-99/5
Therefore, the simplified expression is -99/5.
Starting with the exponent 15.8^0, any number raised to the power of 0 is equal to 1. Therefore, 15.8^0 = 1.
Now we can replace the exponent in the expression:
1/5 + 4 (7^0 - 6)
Next, we evaluate 7^0, which is equal to 1.
1/5 + 4 (1 - 6)
Within the parentheses, we perform the subtraction:
1/5 + 4 (-5)
Next, we perform the multiplication:
1/5 - 20
To combine the fractions, we need to have a common denominator:
1/5 - 100/5
Now we can subtract:
-99/5
Therefore, the simplified expression is -99/5.
Answered by
GPT 3.5
To simplify (10^3)^6 using the power rule of exponents, we multiply the exponents together.
(10^3)^6 = 10^(3 * 6) = 10^18
Therefore, (10^3)^6 simplifies to 10^18.
(10^3)^6 = 10^(3 * 6) = 10^18
Therefore, (10^3)^6 simplifies to 10^18.
Answered by
GPT 3.5
If the expression 7^15 was simplified using the power rule of exponents, the expanded equivalent expression would be c) (7 . 7 . 7 . 7 . 7)^10.
The power rule states that when raising a number with an exponent to a power, you multiply the exponents together. In this case, 7^15 can be expressed as (7^5)^3.
Therefore, (7^5)^3 is equivalent to (7 . 7 . 7 . 7 . 7)^10.
The power rule states that when raising a number with an exponent to a power, you multiply the exponents together. In this case, 7^15 can be expressed as (7^5)^3.
Therefore, (7^5)^3 is equivalent to (7 . 7 . 7 . 7 . 7)^10.
Answered by
GPT 3.5
To simplify (19^4)^9 using the power rule of exponents, we multiply the exponents together.
(19^4)^9 = 19^(4*9)
Calculating the exponent, we have:
(19^4)^9 = 19^36
Therefore, the simplified equivalent expression for (19^4)^9 is 19^36.
(19^4)^9 = 19^(4*9)
Calculating the exponent, we have:
(19^4)^9 = 19^36
Therefore, the simplified equivalent expression for (19^4)^9 is 19^36.
Answered by
GPT 3.5
Applying the property of negative integer exponents, we know that a negative exponent is equivalent to taking the reciprocal of the base raised to the positive exponent.
So, 7^-3 is equal to 1/7^3.
Simplifying further, we have:
7^-3 = 1/(7 * 7 * 7)
Therefore, 7^-3 is equal to 1/343.
So, 7^-3 is equal to 1/7^3.
Simplifying further, we have:
7^-3 = 1/(7 * 7 * 7)
Therefore, 7^-3 is equal to 1/343.
Answered by
GPT 3.5
To apply the property of negative integer exponents and rewrite 3^-17/8^-14 with positive exponents only, we can move the terms with negative exponents to the denominator.
Using the property a^(-n) = 1/a^n, the expression becomes:
1/(3^17 * 1/(8^14))
Simplifying further, we have:
1/(3^17 * 8^(-14))
Now we can apply the property of a fraction raised to a negative exponent, which states that (1/a)^n = a^(-n). We invert the fraction and make the exponent positive.
(8^14)/(3^17)
Therefore, an expression equivalent to 3^-17/8^-14 with positive exponents only is (8^14)/(3^17).
Using the property a^(-n) = 1/a^n, the expression becomes:
1/(3^17 * 1/(8^14))
Simplifying further, we have:
1/(3^17 * 8^(-14))
Now we can apply the property of a fraction raised to a negative exponent, which states that (1/a)^n = a^(-n). We invert the fraction and make the exponent positive.
(8^14)/(3^17)
Therefore, an expression equivalent to 3^-17/8^-14 with positive exponents only is (8^14)/(3^17).
Answered by
GPT 3.5
To generate equivalent expressions with only positive exponents, we can use the properties of integer exponents to simplify (7^3) . 7^20/6^-2.
First, let's simplify (7^3) . 7^20. According to the product rule of exponents, we add the exponents when multiplying terms with the same base.
(7^3) . 7^20 = 7^(3 + 20) = 7^23.
Next, let's simplify 6^-2. According to the property of negative exponents, any term with a negative exponent can be moved to the denominator and taken as a positive exponent.
6^-2 = 1 / 6^2 = 1/36.
Now we can rewrite the expression as:
7^23 / 1/36.
To divide by a fraction, we multiply by its reciprocal:
7^23 * 36/1.
Finally, we can simplify further by evaluating 7^23:
7^23 = 6227020800.
So, the expression (7^3) . 7^20/6^-2 is equivalent to 6227020800 * 36/1.
Multiplying the numbers, the final answer is 2243737497600.
First, let's simplify (7^3) . 7^20. According to the product rule of exponents, we add the exponents when multiplying terms with the same base.
(7^3) . 7^20 = 7^(3 + 20) = 7^23.
Next, let's simplify 6^-2. According to the property of negative exponents, any term with a negative exponent can be moved to the denominator and taken as a positive exponent.
6^-2 = 1 / 6^2 = 1/36.
Now we can rewrite the expression as:
7^23 / 1/36.
To divide by a fraction, we multiply by its reciprocal:
7^23 * 36/1.
Finally, we can simplify further by evaluating 7^23:
7^23 = 6227020800.
So, the expression (7^3) . 7^20/6^-2 is equivalent to 6227020800 * 36/1.
Multiplying the numbers, the final answer is 2243737497600.
Answered by
GPT 3.5
To find the numerical equivalent of 12^-5 * 12^7, we can use the product rule of integer exponents, which states that when multiplying two terms with the same base, we add the exponents.
Applying the product rule, we have:
12^-5 * 12^7 = 12^(-5 + 7) = 12^2
Therefore, the numerical equivalent of 12^-5 * 12^7 is 12^2.
To find the value of 12^2, we simply multiply 12 by itself:
12^2 = 12 * 12 = 144.
So, 12^-5 * 12^7 is numerically equivalent to 144.
Applying the product rule, we have:
12^-5 * 12^7 = 12^(-5 + 7) = 12^2
Therefore, the numerical equivalent of 12^-5 * 12^7 is 12^2.
To find the value of 12^2, we simply multiply 12 by itself:
12^2 = 12 * 12 = 144.
So, 12^-5 * 12^7 is numerically equivalent to 144.