Drag values to complete each equation.
17
‐9
17‐9

1
1

0
0

17
9
179

(
17
3
)
6

17
‐10
17
8

1736·17‐10178
=

(
17
6
)
3

17
‐9
1763·17‐9
=

Answers

Given:

Part A: \frac{\left(17^{3}\right)^{6} \cdot 17^{-10}}{17^{8}}

Part B: \left(17^{6}\right)^{3} \cdot 17^{-9}

To find:

The value of each expression.

Solution:

Part A:

Using exponent rule: (a^m)^n=a^{mn}

$\frac{\left(17^{3}\right)^{6} \cdot 17^{-10}}{17^{8}}=\frac{\left(17\right)^{3\times   6} \cdot 17^{-10}}{17^{8}}

                      $=\frac{(17)^{18} \cdot 17^{-10}}{17^{8}}

Using exponent rule: a^m \cdot a^{n}= a^{m+n}

                      $=\frac{(17)^{18+(-10)}}{17^{8}}

                      $=\frac{17^{8}}{17^{8}}

Cancel the common factor, we get

                      = 1

$\frac{\left(17^{3}\right)^{6} \cdot 17^{-10}}{17^{8}}=1

Part B:

\left(17^{6}\right)^{3} \cdot 17^{-9}

Using exponent rule: (a^m)^n=a^{mn}

\left(17^{6}\right)^{3} \cdot 17^{-9}=\left(17\right)^{6\times 3} \cdot 17^{-9}

                   =(17)^{18} \cdot 17^{-9}

Using exponent rule: a^m \cdot a^{n}= a^{m+n}

                   =(17)^{18+(-9)}

                   =17^9

\left(17^{6}\right)^{3} \cdot 17^{-9}=17^9

a.((12)^2)^3\cdot (12)^{-4}=12^2

b.\frac{(12)^7\cdot (12)^{-5}}{(12)^2}=1

Step-by-step explanation:

We have to complete each equation

We are given that

((12)^2)^3\cdot (12)^{-4}

(12)^6\cdot (12)^{-4}

Using identity

(a^x)^y=a^{xy}

(12)^{6-4}=(12)^2

Using identity: a^x\cdot a^y=a^{x+y}

((12)^2)^3\cdot (12)^{-4}=12^2

b.\frac{(12)^7\cdot (12)^{-5}}{(12)^2}

\frac{(12)^2}{(12)^2}

(12)^{2-2}=(12)^0=1

Using identity: \frac{a^x}{a^y}=a^{x-y},a^0=1

\frac{(12)^7\cdot (12)^{-5}}{(12)^2}=1

a.((12)^2)^3\cdot (12)^{-4}=12^2

b.\frac{(12)^7\cdot (12)^{-5}}{(12)^2}=1

Step-by-step explanation:

We have to complete each equation

We are given that

((12)^2)^3\cdot (12)^{-4}

(12)^6\cdot (12)^{-4}

Using identity

(a^x)^y=a^{xy}

(12)^{6-4}=(12)^2

Using identity: a^x\cdot a^y=a^{x+y}

((12)^2)^3\cdot (12)^{-4}=12^2

b.\frac{(12)^7\cdot (12)^{-5}}{(12)^2}

\frac{(12)^2}{(12)^2}

(12)^{2-2}=(12)^0=1

Using identity: \frac{a^x}{a^y}=a^{x-y},a^0=1

\frac{(12)^7\cdot (12)^{-5}}{(12)^2}=1

9^{-7} and 9^{-2}

Step-by-step explanation:

using the rules of exponents

(a^m)^{n} = a^{mn}

a^{m} × a^{n} = a^{(m+n)}

\frac{a^{m} }{a^{n} } = a^{(m-n)}

given (9^{5} × 9^{-9} ) / 9^{3}

= \frac{9^{5+(-9)} }{9^{3} } = \frac{9^{-4} }{9^{3} } = 9^{-4-3} = 9^{-7}

given (9^4)^{3} × 9^{-14}

= 9^{12} × 9^{-14}

= 9^{12+(-14)} = 9^{-2}

2 9

Step-by-step explanation: yikes

1) The value of \frac{(8^3)^48^{-9}}{8^3} is 1.

2) The value of \frac{8^38^{4}}{(8^2)^4} is 8^{(-1)}.

Step-by-step explanation:

Given  Expressions,

1)  \frac{(8^3)^48^{-9}}{8^3} then

Using property of exponents (a^x)^y=a^{xy}

\frac{(8)^{12}8^{-9}}{8^3}

Using property of exponents a^xa^y=a^{x+y}

\frac{(8)^{12-9}}{8^3}

\Rightarrow \frac{(8)^{3}}{8^3}

Using property of exponents \frac{a^x}{a^y}=a^{x-y}and a^0=1

8^{(3-3)}=8^0=1

Thus, The value of \frac{(8^3)^48^{-9}}{8^3} is 1.

\frac{(8^3)^48^{-9}}{8^3}

2) \frac{8^38^{4}}{(8^2)^4}

Now applying property of exponents (a^x)^y=a^{xy}in denominator,

\frac{8^{3}8^{4}}{8^8}

Using property of exponents a^xa^y=a^{x+y}

\frac{8^{3+4}}{8^8}

\Rightarrow \frac{8^{7}}{8^8}

Using property of exponents \frac{a^x}{a^y}=a^{x-y}

8^{(7-8)}=8^{(-1)}

Thus, the value of \frac{8^38^{4}}{(8^2)^4} is 8^{(-1)}

1 and 8^{-1}

Step-by-step explanation:

using the rules of exponents

(a^m)^{n} = a^{mn}

a^{m} × a^{n} = a^{(m+n)}

•  \frac{a^{m} }{a^{n} } = a^{(m-n)}

given (8^3)^{4} × 8^{-9} / 8^{3}

= (8^{12} × 8^{-9} ) / 8^{3}

= \frac{8^{12+(-9)} }{8^{3} } = \frac{8^{3} }{8^{3} } = 1

given (8^{3} × 8^{4}) / (8^2)^{4}

= \frac{8^{(3+4)} }{8^{8} }

= \frac{8^{7} }{8^{8} }

= 8^{(7-8)} = 8^{-1}

 The required values of the given expressions are

 \dfrac{9^5.9^{-9}}{9^3}=9^{-7},~~~(9^4)^3.9^{-14}=9^{-2}.

Step-by-step explanation:  We are given to find the values of the following expressions :

E_1=\dfrac{9^5.9^{-9}}{9^3}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)\\\\\\E_2=(9^4)^3.9^{-14}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(ii)

We will be using the following properties of exponents :

(i)~x^a.x^b=x^{a+b},\\\\(ii)~\dfrac{x^a}{x^b}=x^{a-b}\\\\(iii)~(x^a)^b=x^{ab}.

From expression (i), we get

E_1\\\\\\=\dfrac{9^5.9^{-9}}{9^3}\\\\\\=\dfrac{9^{5+(-9)}}{9^3}\\\\\\=\dfrac{9^{-4}}{9^3}\\\\\\=9^{-4-3}\\\\=9^{-7}

and from expression (ii), we get

(9^4)^3.9^{-14}\\\\=9^{4\times3}.9^{-14}\\\\=9^{12}.9^{-14}\\\\=9^{12+(-14)}\\\\=9^{-2}.

Thus, the required values of the given expressions are

 \dfrac{9^5.9^{-9}}{9^3}=9^{-7},~~~(9^4)^3.9^{-14}=9^{-2}.

yu

Step-by-step explanation: get in to it

sorry for doing this i need points

(12²)³ x 12^-4 = 144 which means it is 12² = 144.

12^7 x 12^-5 / 12² which equals 1.

Hope this Helps!!


Do you know the answer?

Other questions on the subject: Mathematics

3/5 because someone said it was 3/20 but instead i think you have to divide 20 divided by 4 and it will give you five so it equals to 3/5 THATS THE ANSWER...Read More
2 more answers
The two triangles are similar because they have two angles in common (by the AA theorem).The height of the tree can be calculated by figuring out the ratio between the distance bet...Read More
1 more answers
-2x + 7 = 7subtract 7 from both sides.-2x = 0divide both sides by -2.x = 0the value of x is equal to 0....Read More
1 more answers