hi guys another lesson Pio that is grade
7 math partner 2 module 4 laws of
exponents so on previous lesson nothing
is about addition and subtraction of
polynomials Before Time proceeds a
multiplication and division and laws of exponents
exponents
multiplication at division of
polynomials loss of exponents exponents
follow certain rules that help in
simplifying exponential expression which
is product of power
second power of a power third power of a
product third quotient of a power fifth
of a power so products of a power so
multiply two exponents with the same
base you keep the base and add the
exponent so X raised to the power of a
multiplied by X raised to the power of B
is equal to x a plus b exponents
exponents
so for example 2 cubed multiplied by two squared
squared
exponent which is two and three so two
raised to the power of three plus two equals
equals
two three plus two equals five and two
raised to the power of five is equal to 32.
32.
2 raised to the power of 5 is equal to
two times two times two times two times
two so I multiply five times
another example two x cubed multiplied
by three x squared nothing is
numerical coefficient which is two and
three so that is six and then we have
exponent which is three plus two so
three plus two so answer good nothing is
six x
raised to the power of 5.
Second Law is power of a power to raise
a power to another Power multiply the
inner and the outer exponents just like
this one a x raised to the power of a
multiplied by power of B is equal to x a
B for example X raised to the power of 4
squared so X
X
4 times 2.
so x 4 times 2 equals eight again and
three Cube three
so we multiply nothing exponent
three times three equals nine so three
19683 again so you multiplying along and
three nine times six nineteen thousand
six hundred eighty three and lastly a
raised to the power of two x y so a
2x multiplied by y so equals a
a
2 X Y again a
a
third law is power of a product in
raising product to a certain power each
factor is raised to the indicated power
for example 3 times 5 squared so see
three times five squared because erase
more into a certain or into an indicated
power so again three squared
squared
multiplied by 5 squared
squared
so 3 squared is equal to 9. and 5
squared is equal to 25.
and 9 times 25 is equal to 200
25. next is 3p squared Cube so oops sorry
so 3 cubed and then p squared
Cube
again again 3 Cube p squared 2
multiplied by three so
three cubed equals 27 and then 2 times 3
equals P raised to the power of 6.
last example A Squared B Cube
a
squared multiplied by X plus 3 and then B
B cubed
cubed
multiplied by X Plus 3.
so a
2 times x equals 2 x and 2 times 3
equals plus six so a raised to the power
of two X plus six and then B 3 times x equals
equals
three X plus three times three equals
fourth law is quotient of a power when
dividing Powers with the same base
exponents are subtracted instances
letter a x raised to the power of a
divided by B raised to the power of B so
so 2 raised to the power of 6 divided by
2 raised to the power of four so
magnet and a exponent that is 6 minus
four so two
6 minus 4 equals two so two squared is
equal to 4.
another instance is
denominator so for example 2 raised to
the power of four divided by 2 raised to
exponents
so that is two
four minus six is equal to 2 raised to
the power of negative two because see
four minus six is equal to negative two so
so
one two squared is equal to four one
fourth again next is foreign
6 minus 6 is equal to
M raised to the power of 0 and M raised
to the power of 0 is equal to one you
can see any number raised to the power
of zero on kanyang value is always one so
so
number variables into zero and value is
always one
last law is power of a quotient so power
of a quotient is similar to power of a
product both numerator and denominator
are raised to the indicated power so for
example x divided by y raised to the
power of a so X raised to the power of a
and Y raised to the power of a with
where is y is not equal to zero so c y
in this equal to zero so for example
number one
we have here 3x divided by 2y squared so
nothing is
and x squared and then is 2 squared so
parashan distributive property of
division so why squared
squared
so that is 3 squared is equal to 9 9 and
an x squared 9x squared divided by 2
squared is equal to 4 y squared
so yeah another example
2 divided by 3 squared so 2 squared over
3 squared so equals 2 times 2 equals or
2 squared is equal to 2 times 2 so that
is 4 and 3 squared that is 3 times 3 is
equal to nine so four over nine and the
M raised to the power power of 5 and
then N squared divided by P Squared Q
raised to the power of 4 to the fourth
power so that is m
m
5 multiplied by 4
and then n
2 multiplied by 4.
4. over
over e
e
2 multiplied by
4 and then
and then Q for
for
multiplied by four again so
and five times four equals twenty and
then n 2 times 4 equals eight over p
2 times 4 equals eight and then q 4
times 4 equals sixteen
so once I got nothing is M raised to the
power of 20 and raised to the power of 8
divided by P raised to the power of 8
and Q raised to the power of 16. okay so
that's all for today's video guys and
social nothing lesson is multiplication
and division of polynomials
of exponents see you in our next lesson
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