Q1. Simplify the following expression, and rewrite it in an equivalent form with positive
exponents. 24x^3y^-3/72x^-5y^-1
24x 3 y −3
72x −5 y −1
" 24 % 3− −5 −3− −1
= $ ' x ( )y ( )
# 72 &
" 3*8 % 3+5 −3+1
=$
'x y
# 9 *8 &
" 3%
= $ ' x 8 y −2
#9&
" 1 %" x 8 %
= $ '$ 2 '
# 3 &# y &
=
x8
3y 2
Q2. Raise the quantity in parentheses to the indicated exponent, and simplify the resulting
expression. Express answers with positive exponents. (35x^-5y/128x^-5y^4)^3
3
" 35x −5 y %
$
−5 4 '
# 128x y &
3
3
3
(35) ( x −5 ) ( y)
=
3
3
3
(128) ( x −5 ) ( y 4 )
=
42785x −15 y 3
2097152x −15 y12
=
42785y 3
2097152y12
=
42785
2097152y 9
Q3. Raise the quantity in parentheses to the indicated exponent, and simplify the resulting
expression. Express answers with positive exponents. (43x^-4y^4/86x^0y^-5)^3
3
" 43x −4 y 4 %
$
0 −5 '
# 86x y &
3
" x −4 y 4 %
= $ −5 '
# 2y &
3
" y4 y5 %
=$ 4 '
# 2x &
3
" y9 %
=$ 4 '
# 2x &
9 3
(y )
=
(2) ( x )
3
=
y 27
8x12
4 3