maths, exponents?

Question

2 to the power of 4 times 2 to the power of 6 diveded by 2 to the power of seven: i do not know the answer and how do you work it out do you times 6 and 4 then divide by 7???

2 to the power of 15 divided by 2 to the power of 6 : how do you work out the answer?

what happens when there are brackets?

( m to the power of 10 divided by m to the power of 3 ) divide m to the power 3 ???

and:

b to the power of 9 divided by b to the power of 3 does that equel b to the power of 3????

and what do you do for this

( b to power 3) than power of 3?

thanx so much!

Answer 1

another way to do this for practice, or a more visual way of what the 1st answer said, would be to actually write them out, then cancel them. Like [(2^4)*(2^6)]/(2^7) would be: (2*2*2*2)(2*2*2*2*2*2) (aka 2^10, notice the relation between the 2 to the FOUR and 2 to the SIX), then finish it off by dividing by the 2^7, which youll have 10 2s on top, and seven on bottom, so cancel 7 of them, and oyure only left with 3 of the 2s on top, giving you 2^3, which is eight.

and when youre raising a power to a power, multiply the exponants (the (b^3)^3)) would be B^9

Answer 2

a) 2^((4)(2)^6)/2^7=

1st: simplify : = 2 ^ ((4)(64))/2^7

2^6= 2 x 2 x2 x2 x2 x2 = 64 ok????
4 x 64 = 256
therefore
2^256/2^7=?
take the difference of the exponents 256-7= 249

2^256/2^7= 2^249 or 9.046........x 10^74

b) 2^15/2^6=???

again just take the difference of the exponenents:

15-6= 9

so, 2^15/2^6= 2^9 or 512

If the dividend and the divisor has the same base you can just do this method.

C) m^10/m^3= mmmmmmmmmm/mmm
cancel 3m's above and 3 m's below.
there will remain 7 m's above and nothing below.
or equal to m^7...

Answer 3

2^4*2^6/2^7
when you multiply, multiply the base numbers and add the exponents:
2^4 * 2^6
4^10
when you divide, divide the base numbers and subtract the exponents:
4^10 / 2^7
2^3

when there are brackets, you perform that operation first, then exponents, then multiplication, then division, then addition, then subtraction. work from left to right.
(m^10/m^3)/m^3
m^7/m^3
m^4

b^9/b^3 = b^6

(b^3)^3
this is b^3*b^3*b^3 or b^3 cubed
b*9 see example one above

Answer 4

the laws of exponents are as follows
a^m*a^n=a^(m+n)
a^m/a^n=a^(m-n)
(a^m)^n=a^(mn)
a^-m=1/a^m and
a^m=1/a^-m
while multiplying add the powers algebraically i.e. with the signs
while dividing subtract the power of the divisor from the power of the dividend again algebraically
when you take an exponential quantity form the Nr. to the Dr. or the Dr. to the Nr. change the sign of the power
when you raise the power of some exponential quantity multiply the original power with the new power

Answer 5

when multipying add exponents.
when dividing subtract exponents


work the brackets first!!!

You book has explanations and examples

Answer 6

(2^4 * 2^6)/(2^7)
(2^(4 + 6))/(2^7)
(2^10)/(2^7)
2^(10 - 7)
2^3
8

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(2^15)/(2^6) = 2^(15 - 6) = 2^9 = 512

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[(m^10)/(m^3)]/(m^3)
[m^(10 - 3)]/(m^3)
[m^7]/(m^3)
m^(7 - 3)
m^4

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(b^9)/(b^3) = b^(9 - 3) = b^6

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(b^3)^3 = b^(3 * 3) = b^9