Question

Express in Exponential form.

(a) (-2p^3 )^4 (b) (8x^3 )^0

(c) [(3/4)^(-2) ]^3​

Answer 1

Step-by-step explanation:

a)

$= ({ - 2 {p}^{3} })^{4} \\ = 16 {p}^{12}$

b) Any no. to the power 0 is equal to 1; thus there would be no exponential form.

$= {(8 {x}^{3} ) }^{0} \\ = 1$

c)

$= { ({( \frac{3}{4} )}^{ - 2} )}^{3} \\ = {( \frac{3}{4} )}^{ - 6} \\ = {( \frac{4}{3} )}^{6}$

Answer 2

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