Express in Exponential form.
(a) (-2p^3 )^4 (b) (8x^3 )^0
(c) [(3/4)^(-2) ]^3
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Express in Exponential form.
(a) (-2p^3 )^4 (b) (8x^3 )^0
(c) [(3/4)^(-2) ]^3
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Step-by-step explanation:
a)
[tex] = ({ - 2 {p}^{3} })^{4} \\ = 16 {p}^{12} [/tex]
b) Any no. to the power 0 is equal to 1; thus there would be no exponential form.
[tex] = {(8 {x}^{3} ) }^{0} \\ = 1[/tex]
c)
[tex] = { ({( \frac{3}{4} )}^{ - 2} )}^{3} \\ = {( \frac{3}{4} )}^{ - 6} \\ = {( \frac{4}{3} )}^{6} [/tex]
Step-by-step explanation:
1. ((-2p)^3)4 =
by the exponential formula (a^n)^ m = a^mn
(-2p) ^ 3*4 = -2p ^ 12
by the exponential formula (ab)^ n = a^ n * b^n
(-2)^12 * p^ 12
4096 p^12
2. 8x ^3 ^0
by the exponential formula (a)^0 = 1
so, (8x ^3)^0= 1
3. (3/4)^(-2) ^3 =
by the exponential formula (a/b)^-m = b/a^m
hence,
[(4/3)^2 ]^3
by the exponential formula [(a)^m]^n = a^mn
so, (4/3)^6
by the exponential formula (a/b)^m= a^m/ b^m
4^6/3^6 = 4096/729