1. ## indices check

Hiya i have attempted some indices questions, i was just woundering if anyone could check these to make sure im heading in the right direction with this subject. If these are wrong i would be most grateful if someone could correct me. thankyou

simplify:

1. 10^-1 x 64^1/2 x 8^0

=0.8

2. 5a^2b x 2a^1/2b

=10a^5/8b^2

3. 3b^1/2 x 2b^1/2 x 6b^-1

=36b

4. 7pq
14p^2q^-2

=0.5p^-1q^3

5. (3xy)^2
4xy^1/2

=2.25xy^1.5

6. √s^2t^4 x 3√8s^3t^9
st

=8^1/3s^2t^4

7. 2a^1/2b^1/2c^-1/2 x 3a^3/2b^1/2c^3/2

=6a^4/2bc

8. (a^2b^3)^2 x a^-2b^-1

=a^2b^8

9. (5ab)^-2 x 15a^2b^3

= 0.6ab

10. 3x^1/2y^-1 x 5x^3/2y^-2

= 15x^4/2y^-3

11. 3√27p^6q^9
√9pq

= 3^5/6p^5/2q^7/2

2. Originally Posted by daniel123
Hiya i have attempted some indices questions, i was just woundering if anyone could check these to make sure im heading in the right direction with this subject. If these are wrong i would be most grateful if someone could correct me. thankyou

simplify:

1. 10^-1 x 64^1/2 x 8^0

=0.8
Correct

[quote]2. 5a^2b x 2a^1/2b

=10a^5/8b^2
$a^2 x a^{1/2}= a^{2+ 1/2}= a^{5/2}$, not $a^{5/8}$.
Was that a typo?

3. 3b^1/2 x 2b^1/2 x 6b^-1

=36b
$b^{1/2}b^{1/2}b^{-1}= b^{1/2+ 1/2- 1}= b^{1- 1}= b^0= 1$

4. 7pq
14p^2q^-2

=0.5p^-1q^3
correct.

5. (3xy)^2
4xy^1/2

=2.25xy^1.5
Correct.

6. √s^2t^4 x 3√8s^3t^9
st

=8^1/3s^2t^4
It's not clear where the square roots end. Use parentheses.

7. 2a^1/2b^1/2c^-1/2 x 3a^3/2b^1/2c^3/2

=6a^4/2bc
$a^{1/2}a^{3/2}= a^{1/2+ 3/2}= a^2$

8. (a^2b^3)^2 x a^-2b^-1

=a^2b^8
$(b^3)^2(b^{-1})= (b^6)(b^{-1})= b^{6- 1}$

( $(x^a)^b= x^{ab}$, NOT $x^{a^b}$)

9. (5ab)^-2 x 15a^2b^3

= 0.6ab
$a^{-2}a^2= a^{-2+ 2}= a^0= 1$

10. 3x^1/2y^-1 x 5x^3/2y^-2

= 15x^4/2y^-3
4/2= 2 !

11. 3√27p^6q^9
√9pq

= 3^5/6p^5/2q^7/2

Again, it is not clear where the square roots end. Use parentheses.