simplify using properties of exponents?

Question

(6x)x^5

(5/4)^-2

show work please

Answer 1

(6x)x^5
6(x^1*x^5) <-- regroup
6x^(1+5) <-- add the exponents
6x^6

(5/4)^-2
(4/5)^2 <-- negative exponent, invert and make positive
16/25 <-- multiply through

Answer 2

exponents are just the 'to the power of' symbols. e.g x^3 (^3 being to the power of 3) This just means that you multiply x by itself 3 times. So x^3 = x * x * x Now onto the sum. ((1/2)x)*(x^6)*((2y)^4) Break up the equation into two seperate sums. 1/2x*x^6 and (2y)^4 1/2x*x^6 = 1/2 * x * x * x * x * x * x * x = 1/2 * x^7 = 1/2x^7 (2y)^4 = 2^4 * y^4 = 2 * 2 * 2 * 2 * y * y * y * y = 16 * y^4 = 16y^4 The you put the simplified terms back together into an equation. 1/2x^7 * 16y^4 I hope that helped. I tried to explain the calculations, but it may not have been done very well.

Answer 3

6(x^6)

10^(-3) = (10^3)^(-1). That is the reciprocol of 10^3, and
multiplying by the reciprocol of 10^3 is the same as dividing by
10^3.

(5/4)^-2 = (5/4)^2(^-1).
1 / (25 / 4) = 0.16

Answer 4

6x^6

(4/5)^2 = 16/25

Answer 5

1.(6x)x^5
=6X^(1+5)
=6x^6

2.(5/4)^-2
=(4/5)^2
=16/25

Answer 6

How about I won't solve it?

I'll give you examples:

1.)
a * (a^n) = a^(n+1)
q * a * (a^n) = q*[a^(n+1)]
2.)
(a/b)^-n = (a^-n)/(b^-n) = [1/(a^n)]/[1/(b^n)] = (b^n)/(a^n)

If this doesn't help you, then re read the chapter. :)

Good luck