Fully simplify the following:
4
÷
2
⋅
2
⋅
4
÷
(
15
−
7
)
4÷2⋅2⋅4÷(15−7)
To simplify the expression, we follow the order of operations (PEMDAS/BODMAS).
First, we simplify within parentheses:
15 - 7 = 8.
Next, we perform the division and multiplication from left to right:
4 ÷ 2 ⋅ 2 ⋅ 4 ÷ 8.
4 ÷ 2 = 2:
2⋅2⋅4÷8.
Next, we perform the multiplications:
2⋅2⋅4 = 16:
16÷8.
Finally, we do the division:
16 ÷ 8 = 2.
Therefore, the simplified expression is 2.
Match the following numbers with their expanded form.
(
−
7
)
4
=
(−7)
4
=
−
7
4
=
−7
4
=
(
−
14
)
4
=
(−14)
4
=
−
1
4
4
=
−14
4
=
DRAG & DROP THE ANSWER
−
1
⋅
−
14
⋅
−
14
⋅
−
14
⋅
−
14
−1⋅−14⋅−14⋅−14⋅−14
−
1
⋅
−
7
⋅
−
7
⋅
−
7
⋅
−
7
−1⋅−7⋅−7⋅−7⋅−7
−
7
⋅
−
7
⋅
−
7
⋅
−
7
−7⋅−7⋅−7⋅−7
−
14
⋅
−
14
⋅
−
14
⋅
−
14
−14⋅−14⋅−14⋅−14
−7
4
=
−7 × −7 × −7 × −7
=
−1 × −14 × −14 × −14 × −14
=
−14
4
=
−14 × −14 × −14 × −14
Find the missing value for 5−6⋅5?=5125^{-6}\cdot5^?=5^{12}5
−6
⋅5
?
=5
12
.
?=?=?=
To find the missing value, we can use the property of exponents that states:
a^m ⋅ a^n = a^(m+n).
Given that 5^(-6) ⋅ 5^? = 5^12, we can set up the equation:
5^(-6) ⋅ 5^? = 5^12.
Using the property of exponents, we can combine the exponents on the left side of the equation:
5^(-6+?) = 5^12.
To make the bases equal, we set the exponents equal to each other:
-6 + ? = 12.
Simplifying the equation, we get:
? = 12 - (-6),
? = 12 + 6,
? = 18.
Therefore, the missing value is 18.
Simplify 9−2⋅9109^{-2}\cdot9^{10}9
−2
⋅9
10
and write your answer in exponential form. (Example: 525^25
2
not 252525 ).
To simplify 9^(-2) × 9^10, we use the property of exponents which states that a^m × a^n = a^(m+n).
Therefore, 9^(-2) × 9^10 can be simplified as 9^(10+(-2)) = 9^8.
Therefore, the simplified expression in exponential form is 9^8.
Simplify 715⋅7−87^{15}\cdot7^{-8}7
15
⋅7
−8
and write your answer in exponential form. (Example: 525^25
2
not 252525 ).
To simplify 7^15 × 7^(-8), we use the property of exponents that states a^m × a^n = a^(m+n).
So, 7^15 × 7^(-8) can be simplified as 7^(15+(-8)) = 7^7.
Therefore, the simplified expression in exponential form is 7^7.
Simplify the following and leave your answer in exponential form. (Example: write 525^25
2
not 252525 ).
8138−7\frac{8^{13}}{8^{-7}}
8
−7
8
13
To simplify the expression, we can subtract the exponents and keep the base the same:
8^13 ÷ 8^(-7) = 8^(13 - (-7)) = 8^(13 + 7) = 8^20.
Therefore, the simplified expression in exponential form is 8^20.
Simplify the following and leave your answer in exponential form. (Example: write 525^25
2
not 252525 ).
6106\frac{6^{10}}{6}
6
6
10
To simplify the expression, we can subtract the exponent of 6 in the denominator from the exponent of 6 in the numerator:
6^10 ÷ 6^1 = 6^(10 - 1) = 6^9.
Therefore, the simplified expression in exponential form is 6^9.
Simplify (3−5)−7\left(3^{-5}\right)^{-7}(3
−5
)
−7
To simplify the expression, we need to apply the rules of exponents and evaluate the nested exponent first.
The exponent of an exponent rule states that (a^b)^c = a^(b*c).
So, (3^(-5))^(-7) can simplify to 3^(-5 * -7) = 3^35.
Now we can simplify the expression further:
(3-5)^(-7) = (-2)^(-7).
Therefore, the simplified expression in exponential form is (-2)^(-7).
(3^-5)^-7
To simplify the expression (3^(-5))^(-7), we need to evaluate the exponent of an exponent.
The exponent of an exponent rule states that (a^b)^c = a^(b*c).
So, we have (3^(-5))^(-7) = 3^((-5) * (-7)) = 3^35.
Therefore, the simplified expression in exponential form is 3^35.
(x^-8)^-7
To simplify the expression (x^(-8))^(-7), we need to apply the rule of exponents for a negative exponent raised to a negative power.
The rule of exponents for a negative exponent raised to a negative power is: (a^(-b))^(-c) = a^(b*c).
So, we have (x^(-8))^(-7) = x^((-8)*(-7)) = x^56.
Therefore, the simplified expression in exponential form is x^56.
(6^7)^2
To simplify the expression (6^7)^2, we need to apply the rule of exponents for a power raised to another power.
The rule of exponents for a power raised to another power is: (a^b)^c = a^(b*c).
So, we have (6^7)^2 = 6^(7*2) = 6^14.
Therefore, the simplified expression in exponential form is 6^14.
3
−9
⋅3⋅3
−3
=
To simplify the expression 3^(-9) * 3 * 3^(-3), we need to combine the terms with the same base using the power of a product rule.
3^(-9) means taking the reciprocal of 3^9, which gives us 1/3^9.
3^(-3) means taking the reciprocal of 3^3, which gives us 1/3^3.
So, we rewrite the expression as (1/3^9) * 3 * (1/3^3).
Now we can multiply the numerators and denominators together:
(1 * 3 * 1) / (3^9 * 3^3) = 3 / 3^12.
Finally, we simplify further by subtracting the exponents:
3 / 3^12 = 3 / 3^(12-1) = 3 / 3^11.
Therefore, the simplified expression is 3 / 3^11.
3^−9⋅3⋅3^−3 =
To simplify the expression 3^(-9) * 3 * 3^(-3), we can combine the terms with the same base by applying the rule of exponents that states:
a^m * a^n = a^(m + n).
Using this rule, we can rewrite the expression as:
3^(-9 + 1 - 3).
Simplifying the exponents, we get:
3^(-11).
Therefore, the simplified expression is 3^(-11).
its supposed to be a fraction as the final answer
Apologies for the confusion. To simplify the expression 3^(-9) * 3 * 3^(-3) into a fraction form, we can still combine the terms with the same base.
3^(-9) * 3 * 3^(-3) = 3^(-9 + 1 - 3) = 3^(-11).
Since 3^(-11) represents a negative exponent, it means that we need to take the reciprocal of the base raised to the positive exponent. Thus,
3^(-11) = 1 / 3^11.
Therefore, the simplified expression in fraction form is 1 / 3^11.
1/4*1/4*1/4*1/4
To simplify the expression 1/4 * 1/4 * 1/4 * 1/4, we can multiply the numerators and denominators together:
(1 * 1 * 1 * 1) / (4 * 4 * 4 * 4).
Simplifying further, the numerator is 1 and the denominator is 4^4 or 4 raised to the power of 4:
1 / 4^4 = 1 / 256.
Therefore, the simplified expression is 1 / 256.
that is WRONG bruv
Apologies for the mistake.
To simplify 1/4 * 1/4 * 1/4 * 1/4, we can combine the fractions by multiplying the numerators and denominators:
(1 * 1 * 1 * 1) / (4 * 4 * 4 * 4) = 1 / (4^4).
Now, we can simplify the denominator by evaluating 4^4:
4^4 = 4 * 4 * 4 * 4 = 256.
Therefore, the simplified expression is 1/256.
4
1
⋅
4
1
⋅
4
1
⋅
4
1
To simplify 4^1 * 4^1 * 4^1 * 4^1, we can combine the exponents by applying the rule of exponents that states:
a^m * a^n = a^(m + n).
Using this rule, we can add the exponents together:
4^1 * 4^1 * 4^1 * 4^1 = 4^(1 + 1 + 1 + 1).
Simplifying the exponent, we get:
4^(4).
Therefore, the simplified expression is 4^4.
what is that as a fraction
To express 4^1 * 4^1 * 4^1 * 4^1 as a fraction, we can simplify it as:
4^1 * 4^1 * 4^1 * 4^1 = 4^(1+1+1+1) = 4^4.
Since 4^4 represents the exponentiation of 4 raised to the power of 4, we can write it as a fraction with 1 as the numerator:
1/4^4 = 1/256.
Therefore, the expression 4^1 * 4^1 * 4^1 * 4^1 as a fraction is 1/256.
(
y
3
y
5
)
2
⋅(
y
5
y
7
)
5
To simplify the expression (y^3 * y^5)^2 * (y^5 * y^7)^5, we can apply the rules of exponents.
First, within each set of parentheses, we can combine the terms with the same base:
(y^3 * y^5)^2 can be simplified as y^(3+5)^2 = y^8.
Similarly, (y^5 * y^7)^5 can be simplified as y^(5+7)^5 = y^60.
Now, we can multiply the two simplified expressions:
(y^8) * (y^60) = y^(8+60) = y^68.
Therefore, the simplified expression is y^68.
(y^5/y^3)^2*(y^7/y^5)^5
To simplify the expression (y^5/y^3)^2 * (y^7/y^5)^5, we can simplify within each set of parentheses and then multiply.
Within the first set of parentheses, (y^5/y^3)^2, we can divide the terms with the same base:
(y^5/y^3)^2 = y^(5-3)^2 = y^2^2 = y^4.
Similarly, within the second set of parentheses, (y^7/y^5)^5, we can divide the terms with the same base:
(y^7/y^5)^5 = y^(7-5)^5 = y^2^5 = y^10.
Now, we can multiply the two simplified expressions:
(y^4) * (y^10) = y^(4 + 10) = y^14.
Therefore, the simplified expression is y^14.
(x^3)^7*x^8
To simplify the expression (x^3)^7 * x^8, we can apply the rule of exponents for a power raised to another power.
The rule states that (a^b)^c = a^(b*c).
Applying this rule, we have:
(x^3)^7 = x^(3*7) = x^21.
Now, we can multiply the simplified expression by x^8:
x^21 * x^8 = x^(21+8) = x^29.
Therefore, the simplified expression is x^29.
(x^-4*x^6)^2
To simplify the expression (x^(-4) * x^6)^2, we can combine the terms with the same base using the exponent addition rule.
In the parentheses, we multiply x^(-4) and x^6:
(x^(-4) * x^6)^2 = x^(-4+6)^2 = x^2^2 = x^4.
Therefore, the simplified expression is x^4.
(x^-7*x^5)^3/(x^2*x^3)^2
To simplify the expression (x^-7 * x^5)^3 / (x^2 * x^3)^2, we can simplify the terms within the parentheses first.
In the numerator, we multiply x^-7 and x^5:
(x^-7 * x^5)^3 = x^(-7+5)^3 = x^-2^3 = x^-6.
In the denominator, we multiply x^2 and x^3:
(x^2 * x^3)^2 = x^(2+3)^2 = x^5^2 = x^10.
Now, we can divide the numerator by the denominator:
(x^-6) / (x^10) = x^(-6-10) = x^-16.
Therefore, the simplified expression is x^-16.
bro thats wrong is has to have a postitive exponent
Apologies for the error. Let's correct the simplification.
To simplify the expression (x^-7 * x^5)^3 / (x^2 * x^3)^2, let's simplify the terms within the parentheses first.
In the numerator, we multiply x^-7 and x^5:
(x^-7 * x^5)^3 = x^(-7*3) * x^(5*3) = x^-21 * x^15.
In the denominator, we multiply x^2 and x^3:
(x^2 * x^3)^2 = x^(2*2) * x^(3*2) = x^4 * x^6.
Now, we can divide the numerator by the denominator:
(x^-21 * x^15) / (x^4 * x^6) = x^(-21 + 15) / x^(4 + 6) = x^-6 / x^10 = 1/x^6 * 1/x^10 = 1 / (x^6 * x^10) = 1 / x^16.
Therefore, the simplified expression is 1/x^16.
Students were given the task to fully simplify
(2^2*2^-6)^-3*(2)^0
John believes the answer was 1 as any number to the zero power (except 0^0 ) equals 1.
Carol believes that the answer is 4^12 since
2*2=4 and for the exponents 2+-6=-4 and -4*-3=12
What is John's error?
What is Carol's error?
What is the correct answer. Show your work.
Math