Question

Express 64^3 with a base of 4. Express (-27)^5 with a base of 3.

Answer 1

Answer: 4^9

(-3)^15

Step-by-step explanation:

64^3

Connect like this:

64 = 8×8 == 4×2×4×2== 4×4×4

[Yay, 64 is the cube of 4, right? ]

64 == 4^3

Now what does 64^3 mean? It means 64 is multiplied 3 times which in turn means 4^3 is multiplied 3 times or 4 is multiplied 9 times.

64^3 == (4^3)^3 == 4^9

[Law of exponents : [a^m]^n = a^(m×n)

(-27)^5

We know 27 = 3^3

-27 = - 3^3

(-27)^5 == (-3^3)^5 = (-3)^15

[Refer exponent law of above question]

Answer 2

Answer:

HEY THERE!!

Step-by-step explanation:

4 X 4 X 4 =64

64^3 CAN ALSO BE WRITTEN AS ((4^3)^3)

=4^(3*3)

= 4^9

-3 X -3 X -3 = -27

-27^5 CAN ALSO BE WRITTEN AS ((-3^3)^5)

= -3^(15)

FORMULA: (A^M)^N = A^(M*N)