SOLUTION: a.(a b^2) ^5 simplify b. (2x)^2 x (2x)^4 simplify c.(m^3 n^2) ^3 d. 2^5 x 2^-7/2^3

Question 347928: a.(a b^2) ^5 simplify
b. (2x)^2 x (2x)^4 simplify
c.(m^3 n^2) ^3
d. 2^5 x 2^-7/2^3
Answer by haileytucki(390) (Show Source): You can put this solution on YOUR website!
A.
(ab^(2))^(5)
Expand the exponent (5) to the expression.
a^(5)b^(2*5)
Multiply 2 by 5 to get 10.
a^(5)b^(10)
B.(2x)^(2)(2x)^(4)
Expand the exponent (2) to the expression.
2^(2)x^(2)(2x)^(4)
Squaring a number is the same as multiplying the number by itself (2*2). In this case, 2 squared is 4.
4x^(2)(2x)^(4)
Expand the exponent (4) to the expression.
(4x^(2))*2^(4)x^(4)
Raising a number to the 4th power is the same as multiplying the number by itself 4 times. In this case, 2 raised to the 4th power is 16.
(4x^(2))*16x^(4)
Multiply 16x^(4) by each term inside the parentheses.
64x^(6)

C.
(m^(3)n^(2))^(3)
Expand the exponent (3) to the expression.
m^(3*3)n^(2*3)
Multiply 3 by 3 to get 9.
m^(9)n^(2*3)
Multiply 2 by 3 to get 6.
m^(9)n^(6)

D.
2^(5)*(2^(-7))/(2^(3))
Raising a number to the 5th power is the same as multiplying the number by itself 5 times. In this case, 2 raised to the 5th power is 32.
32*(2^(-7))/(2^(3))
To divide 2^(-7) by 2^(3), subtract the denominator exponent from the numerator exponent.
32*2^(-7-3)
Subtract 3 from -7 to get -10.
32*2^(-10)
Remove the negative exponent by rewriting 2^(-10) as (1)/(2^(10)). A negative exponent follows the rule a^(-n)=(1)/(a^(n)).
32*(1)/(2^(10))
Raising a number to the 10th power is the same as multiplying the number by itself 10 times. In this case, 2 raised to the 10th power is 1024.
32*(1)/(1024)
Cancel the common factor of 32 from the first term 32 and the denominator of the second term (1)/(1024).
1*(1)/(32)
Multiply 1 by (1)/(32) to get (1)/(32).
(1)/(32)
The approximate value of 2^(5)*(2^(-7))/(2^(3)) is 0.03.
0.03
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