Math Help Please ASAP?

Question

Rewrite the following expressions as a power with a single base, then
evaluate.
a) (–10)^3× (–10)^2
b) ( 2 )^5( 2 )( 2 )^2
c) 3^15/3^11
d)( -2)^10/(-2)3
e)[(−1 )^4 ] ^5 )
f)[[1/4]^2]^3

Answer 1

a)

The given expression as a power with a single base

   (-10)³×(-10)²

Apply the power rule

= (-10)³ + 2

= (-10)⁵ .

Answer 2

b)

The given expression as a power with a single base

(2)⁵(2)(2)²

 Apply the power rule

= (2)^{5 +2 + 1}

= (2)⁸ .

 

Answer 3

c)

3¹⁵ / 3¹¹

Apply the power rule

= 3^{15 - 11}

= 3⁴.

Answer 4

d)

(-2)¹⁰ / (-2)³

Apply the power rule

= (-2)^{10 - 3}

= (-2)⁷.

 

 

Answer 5

e)

[(-1)⁴]⁵

Apply the power rule

(-1)^4*5

(-1)²⁰.

Answer 6

f)

   [ 1 / 4]²]³

Apply the power rule

= [1 / 4]^2*3

= [ 1 / 4]⁶.