Question

Fully simplify the following:
4
÷
2
⋅
2
⋅
4
÷
(
15
−
7
)
4÷2⋅2⋅4÷(15−7)

Answer 1

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

Answer 2

Find the missing value for 5−6⋅5?=5125^{-6}\cdot5^?=5^{12}5
−6
⋅5
?
=5
12
.



?=?=?=

Answer 3

Simplify 9−2⋅9109^{-2}\cdot9^{10}9
−2
⋅9
10
and write your answer in exponential form. (Example: 525^25
2
not 252525 ).

Answer 4

Simplify 715⋅7−87^{15}\cdot7^{-8}7
15
⋅7
−8
and write your answer in exponential form. (Example: 525^25
2
not 252525 ).

Answer 5

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

​

Answer 6

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

​

Answer 7

Simplify (3−5)−7\left(3^{-5}\right)^{-7}(3
−5
)
−7

Answer 8

(3^-5)^-7

Answer 9

(x^-8)^-7

Answer 10

(6^7)^2

Answer 11

3
−9
⋅3⋅3
−3
=

Answer 12

3^−9⋅3⋅3^−3 =

Answer 13

its supposed to be a fraction as the final answer

Answer 14

1/4*1/4*1/4*1/4

Answer 15

that is WRONG bruv

Answer 16

4
1
​
⋅
4
1
​
⋅
4
1
​
⋅
4
1
​

Answer 17

what is that as a fraction

Answer 18

(
y
3

y
5

​
)
2
⋅(
y
5

y
7

​
)
5

Answer 19

(y^5/y^3)^2*(y^7/y^5)^5

Answer 20

(x^3)^7*x^8

Answer 21

(x^-4*x^6)^2

Answer 22

(x^-7*x^5)^3/(x^2*x^3)^2

Answer 23

bro thats wrong is has to have a postitive exponent

Answer 24

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

Answer 25

answer gpt

Answer 26

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.

Answer 27

−7
4
=
−7 × −7 × −7 × −7
=
−1 × −14 × −14 × −14 × −14
=
−14
4
=
−14 × −14 × −14 × −14

Answer 28

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.

Answer 29

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.

Answer 30

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.

Answer 31

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.

Answer 32

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.

Answer 33

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).

Answer 34

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.

Answer 35

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.

Answer 36

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.

Answer 37

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.

Answer 38

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).

Answer 39

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.

Answer 40

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.

Answer 41

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.

Answer 42

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.

Answer 43

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.

Answer 44

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.

Answer 45

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.

Answer 46

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.

Answer 47

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.

Answer 48

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.

Answer 49

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.