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A) 5^4×5^8= 5^4+8=5^12
B) 3^-3×3^7= 3^-3+7=3^4
C) d^9×d^-3=d^9-3= d^6
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There is a rule in exponents that if the base is the same then we can add or subtract(based on the signs)when there is a multiplication or division between them.
This rule can be applied here also...
The first sum can be done this way...
a. 5^1 x 5^8 = 5^(1+8)=5^9
b.3^-3 x 3^7
now you need to always add when it is multiplication and subtract when it is division.
always keep the exponents in the same order. Don't change their positions.
now just put the other exponent in a bracket so that it won't be confusing.
so, this is how you do it:
3^[-3+(7)]
=3^4
c.d^9 x d^-3
do the same...
d^[9+(-3)]
=d^6
I hope this helps...
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