0:02 hi guys another lesson Pio that is grade
0:06 7 math partner 2 module 4 laws of
0:07 exponents so on previous lesson nothing
0:09 is about addition and subtraction of
0:11 polynomials Before Time proceeds a
0:14 multiplication and division and laws of exponents
0:17 exponents
0:20 multiplication at division of
0:23 polynomials loss of exponents exponents
0:25 follow certain rules that help in
0:27 simplifying exponential expression which
0:35 is product of power
0:38 second power of a power third power of a
0:42 product third quotient of a power fifth
0:52 of a power so products of a power so
0:54 multiply two exponents with the same
0:57 base you keep the base and add the
1:00 exponent so X raised to the power of a
1:02 multiplied by X raised to the power of B
1:07 is equal to x a plus b exponents
1:09 exponents
1:12 so for example 2 cubed multiplied by two squared
1:15 squared
1:23 exponent which is two and three so two
1:26 raised to the power of three plus two equals
1:28 equals
1:32 two three plus two equals five and two
1:35 raised to the power of five is equal to 32.
1:37 32.
1:40 2 raised to the power of 5 is equal to
1:42 two times two times two times two times
1:45 two so I multiply five times
1:48 another example two x cubed multiplied
1:52 by three x squared nothing is
1:55 numerical coefficient which is two and
1:57 three so that is six and then we have
2:06 exponent which is three plus two so
2:10 three plus two so answer good nothing is
2:12 six x
2:16 raised to the power of 5.
2:19 Second Law is power of a power to raise
2:21 a power to another Power multiply the
2:23 inner and the outer exponents just like
2:25 this one a x raised to the power of a
2:29 multiplied by power of B is equal to x a
2:32 B for example X raised to the power of 4
2:35 squared so X
2:36 X
2:40 4 times 2.
2:44 so x 4 times 2 equals eight again and
2:52 three Cube three
2:59 so we multiply nothing exponent
3:01 three times three equals nine so three
3:11 19683 again so you multiplying along and
3:14 three nine times six nineteen thousand
3:17 six hundred eighty three and lastly a
3:22 raised to the power of two x y so a
3:27 2x multiplied by y so equals a
3:32 a
3:37 2 X Y again a
3:39 a
3:42 third law is power of a product in
3:45 raising product to a certain power each
3:47 factor is raised to the indicated power
3:59 for example 3 times 5 squared so see
4:02 three times five squared because erase
4:04 more into a certain or into an indicated
4:07 power so again three squared
4:09 squared
4:12 multiplied by 5 squared
4:13 squared
4:18 so 3 squared is equal to 9. and 5
4:21 squared is equal to 25.
4:25 and 9 times 25 is equal to 200
4:31 25. next is 3p squared Cube so oops sorry
4:39 so 3 cubed and then p squared
4:44 Cube
4:48 again again 3 Cube p squared 2
4:51 multiplied by three so
4:55 three cubed equals 27 and then 2 times 3
4:59 equals P raised to the power of 6.
5:02 last example A Squared B Cube
5:08 a
5:13 squared multiplied by X plus 3 and then B
5:14 B cubed
5:15 cubed
5:20 multiplied by X Plus 3.
5:23 so a
5:26 2 times x equals 2 x and 2 times 3
5:30 equals plus six so a raised to the power
5:35 of two X plus six and then B 3 times x equals
5:36 equals
5:39 three X plus three times three equals
5:46 fourth law is quotient of a power when
5:48 dividing Powers with the same base
5:50 exponents are subtracted instances
5:58 letter a x raised to the power of a
6:01 divided by B raised to the power of B so
6:16 so 2 raised to the power of 6 divided by
6:19 2 raised to the power of four so
6:23 magnet and a exponent that is 6 minus
6:25 four so two
6:28 6 minus 4 equals two so two squared is
6:30 equal to 4.
6:34 another instance is
6:40 denominator so for example 2 raised to
6:43 the power of four divided by 2 raised to
6:47 exponents
6:50 so that is two
6:53 four minus six is equal to 2 raised to
6:55 the power of negative two because see
6:57 four minus six is equal to negative two so
6:58 so
7:11 one two squared is equal to four one
7:14 fourth again next is foreign
7:25 6 minus 6 is equal to
7:28 M raised to the power of 0 and M raised
7:31 to the power of 0 is equal to one you
7:33 can see any number raised to the power
7:35 of zero on kanyang value is always one so
7:36 so
7:41 number variables into zero and value is
7:42 always one
7:46 last law is power of a quotient so power
7:48 of a quotient is similar to power of a
7:50 product both numerator and denominator
7:53 are raised to the indicated power so for
7:55 example x divided by y raised to the
7:58 power of a so X raised to the power of a
8:00 and Y raised to the power of a with
8:03 where is y is not equal to zero so c y
8:05 in this equal to zero so for example
8:06 number one
8:11 we have here 3x divided by 2y squared so
8:14 nothing is
8:25 and x squared and then is 2 squared so
8:28 parashan distributive property of
8:36 division so why squared
8:38 squared
8:43 so that is 3 squared is equal to 9 9 and
8:47 an x squared 9x squared divided by 2
8:51 squared is equal to 4 y squared
8:54 so yeah another example
8:59 2 divided by 3 squared so 2 squared over
9:03 3 squared so equals 2 times 2 equals or
9:05 2 squared is equal to 2 times 2 so that
9:08 is 4 and 3 squared that is 3 times 3 is
9:12 equal to nine so four over nine and the
9:14 M raised to the power power of 5 and
9:17 then N squared divided by P Squared Q
9:20 raised to the power of 4 to the fourth
9:23 power so that is m
9:24 m
9:27 5 multiplied by 4
9:30 and then n
9:33 2 multiplied by 4.
9:34 4. over
9:36 over e
9:37 e
9:40 2 multiplied by
9:43 4 and then
9:46 and then Q for
9:47 for
9:53 multiplied by four again so
9:56 and five times four equals twenty and
10:02 then n 2 times 4 equals eight over p
10:06 2 times 4 equals eight and then q 4
10:09 times 4 equals sixteen
10:11 so once I got nothing is M raised to the
10:14 power of 20 and raised to the power of 8
10:17 divided by P raised to the power of 8
10:20 and Q raised to the power of 16. okay so
10:21 that's all for today's video guys and
10:23 social nothing lesson is multiplication
10:26 and division of polynomials
10:29 of exponents see you in our next lesson
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