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